cbse ncert solutions for class 11 mathematics chapter 09 · 2019. 11. 27. · back of chapter...
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Exercise 9.1
1. Write the first five terms of the sequences whose term is .
Hint: Put .
Solution:
Solution step 1:
Putting , and we get
So, the required first five terms are and
2. Write the first five terms of the sequences whose term is
Hint: Put .
Solution:
Solution step 1:
Putting , we get
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CBSE NCERT Solutions for Class 11 Mathematics Chapter 09
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So, the required first five terms are
3. Write the first five terms of the sequences whose term is
Hint: Put .
Solution:
Solution step 1:
Putting , we get
So, the required first five terms are and
4. Write the first five terms of the sequences whose term is
Hint: Put .
Solution:
Solution step 1: Putting , we get
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So, the required first five terms are. .
5. Write the first five terms of the sequences whose term is
Hint: Put .
Solution:
Solution step 1: Putting , we get
So, the required first five terms are , and
6. Write the first five terms of the sequences whose term is
Hint: Put .
Solution:
Solution step 1: Putting , we get
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So, the required first five terms are .
7. Find the and term in the following sequence whose term is
Hint: Put .
Solution:
Solution step 1: Putting , we get
Substituting , we get
8. Find the term in the following sequence whose term is
Hint: Put .
Solution:
Solution step 1: Putting , we get
9. Find the term in the following sequence whose term is
Hint: Put .
Solution:
Solution step 1: Putting , we get
10. Find the term in the following sequence whose term is
Hint: Put .
Solution:
Solution step 1: Substituting , we obtain
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11. Write the first five terms of the following sequence and obtain the corresponding series:
for all
Hint: Put and use the previous term wisely.
Solution:
Solution step 1: for all
Hence, the first five terms of the sequence are and .
So the series is
12. Write the first five terms of the following sequence and obtain the corresponding series:
Hint: Put and use the previous term wisely.
Solution:
Solution step 1:
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Hence, the first five terms of the sequence are
So the series is
13. Write the first five terms of the following sequence and obtain the corresponding series:
Hint: Put and use the previous term wisely.
Solution:
Solution step 1:
Hence, the first five terms of the sequence are and
So the series is
14. The Fibonacci sequence is defined by
Find , for
Hint: Put and use the previous term wisely.
Solution:
Solution step 1:
For
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For
For
For
For
Exercise 9.2
1. Find the sum of odd integers from 1 to 2001.
Hint: and
Solution:
Solution step 1: The odd integers from to are It is in A.P.
So, first term,
Difference between 2 numbers,
Here,
So, the sum of odd numbers from to is
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2. Find the sum of all natural numbers lying between and , which are multiples of .
Hint: and
Solution:
Solution step 1: So the series is .
So
So, the sum of all natural numbers lying between and , which are multiples of , is .
3. In an A.P, the first term is and the sum of the first five terms is one‐fourth of the next five terms.
Show that term is
Hint:
Solution:
Solution step 1:First term
Let be the difference betweentwo numbers of the A.P.
So, the A. P. is .
Sum of first five terms
Sum of next five terms
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[by question]
So, the of the A.P. is
4. How many terms of the A.P. are needed to give the sum ?
Hint:
Solution:
Solution step 1: Assume number of terms first term, and common difference
Here, [By question]
Sum of all term in A.P.=
[ ]
or
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5. In an A.P., if term is and term is , prove that the sum of first terms is ,
where
Solution:
Solution step 1:
Using the above formula term will be
term
term
By subtracting from , we get
Putting the value of in , we get
So, the sum of first terms of the A.P. is. .
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6. If the sum of a certain number of terms of the A.P. is Find the last term
Hint: and
Solution:
Solution step 1: Sum of all term of A.P. is 116.
And, and
Putting the values in above formula we get
or
n should be a integer, so
Last term
So, the last term of the A.P. is .
7. Find the sum to terms of the A.P., whose term is
Hint: and
Solution:
Solution step 1: term a
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So
Comparing the coefficient of , we get
8. If the sum of terms of an A.P. is , where and are constants find the common
difference.
Hint: Sum of n number in A.P.
Solution:
Solution step 1: Sum of all number in A.P.:
So [By question]
Comparing the coefficients of on both sides, we get
So, the common difference of the A.P. is
9. The sums of terms of two arithmetic progressions are in the ratio . Find the ratio of
their terms.
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Hint: The general term in A.P.
Solution:
Solution step 1: Assume first terms and be as common difference of A.P.
Putting in , we get
By equation and , we get
So, the ratio of term of both the A.P.S is
10. If the sum of first terms of an A.P. is equal to the sum of the first terms, then find the sum of the
first terms.
Hint: The general term in A.P. , Sum of n number in
A.P.
Solution:
Solution step 1: Assume a be as first term and d be as common difference of A.P.
The general term in A.P.
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Using the above formula and are
Sum of n number in A.P.
Using the above formula
[ By question]
So, the sum of the first terms of the A.P. is
11. Sum of the first and terms of an A.P. are and , respectively.
Prove that
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Hint: The general term in A.P. , Sum of n number in
A.P.
Solution:
Solution step 1: Assume a be as first term and d be as common difference of A.P.
Sum of n number in A.P.
According to the above formula and are:
[ by question]
[ by question]
[ by question]
Subtracting from , we get
Subtracting from , we get
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By equation (iv) and (v) we get
[Dividing both sides by ]
Hence proved.
12. The ratio of the sums of and terms of an A.P. is . Show that the ratio of and term
is .
Hint: Sum of n number in A.P. ,The general term in A.P.
Solution:
Solution step 1: Assume a be as first term and d be as common difference of A.P.
Sum of n number in A.P.
Using the above formula we get:
Putting and in , we get
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The general term in A.P.
Using the above formula we get:
From and , we get
Hence proved.
13. If the sum of terms of an A.P. is and its term is find the value of
Hint: Sum of n number in A.P. ,The general term in A.P.
Solution:
Solution step 1: Assume a be as first term and d be as common difference of A.P.
The general term in A.P.
Using the above formula we get:
Sum of n number in A.P.
Using the above formula we get:
Comparing the coefficient of on both sides, we get
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Comparing the coefficient of on both sides, we obtain
So, from equation , we get
So, the value of is .
14. Insert five numbers between and such that the resulting sequence is an A. P.
Hint: Sum of n number in A.P. ,The general term in A.P.
Solution:
Solution step 1: Assume and be five numbers between and .
So, a
The general term in A.P.
Using the above formula we get:
So, the five numbers are and
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15. If is the A.M. between and , then find the value of
Hint: A. M. of and
Solution:
Solution step 1: A. M. of and
[ ]
So, the required value of n is 1.
16. Between and , numbers have been inserted in such a way that the resulting sequence is an
A.P. and the ratio of and numbers is Find the value of
Hint: Sum of n number in A.P. ,The general term in A.P.
Solution:
Solution step 1: Assume , be numbers such that is an A.P.
So,
The general term in A.P.
Using the above formula we get:
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According to the given condition,
So, the required value of m is 14.
17. A man starts repaying a loan as first installment of ₹ . If he increases the installment by Rs
every month, what amount he will pay in the installment?
Hint: Sum of n number in A.P. ,The general term in A.P.
Solution:
Solution step 1: The first installment of the loan is₹100 and the second installment of the loan is
₹ and so on.
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So the A. P. is
So,
The general term in A.P.
Using the above formula we get:
So, the installment is Rs .
18. The difference between any two consecutive interior angles of a polygon is . If the smallest angle
is , find the number of the sides of the polygon.
Hint: Sum of all angles of a polygon with sides is ,Sum of n number in
A.P.
Solution:
Solution step 1: The angles of the polygon will form an A.P. So the A.P. will be
Sum of all angles of a polygon with sides is
Sum of n number in A.P.
By using the equation (i) and (ii) we get:
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or
Exercise 9.3
1. Find the and terms of the G.P.
Hint:
Solution:
Solution step 1: G.P. is
So, first term , common ratio
Using the above formula and will be:
2. Find the term of a G.P. whose term is 192 and the common ratio is
Hint:
Solution:
Solution step 1: Assume a be the first term and r be the common ratio of the G.P.
So common ratio,
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By using the above formula we get:
So the required term is .
3. The and terms of a G.P. are and , respectively. Show that
Hint:
Solution:
Solution step 1: Assume a be the first term and r be the common ratio of the G.P.
By using the above equation we get:
Dividing equation by , we get
Dividing equation by , we get
From equation and , we get
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Hence proved.
4. The term of a G.P. is square of its second term, and the first term is Determine its term.
Hint:
Solution:
Solution step 1: Assume a be the first term and r be the common ratio of the G.P.
[ By question]
Using the above formula we get:
[ By question]
So, the term of the G.P. is
5. Which term of the following sequences:
, is ?
Hint:
Solution:
(a) The given sequence is , is 128?
Solution step 1: Assume a be the first term and r be the common ratio of the G.P.
So, and
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term= . [ By question]
Using the above formula we get:
So, the term is
, is 729?
(b) The given sequence is
Hint:
Solution:
Solution step 1: Assume a be the first term and r be the common ratio of the G.P.
So, and
term= . [ By question]
Using the above formula we get:
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So, the term is
, is ?
(c) The given sequence is
Hint:
Solution:
Solution step 1: Assume a be the first term and r be the common ratio of the G.P.
So,
term = . [ By question]
Using the above formula we get:
So, the term is. .
6. For what values of , the numbers are in G.P?
Hint:
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Solution:
Solution step 1: Numbers are [ By question]
Common ratio
Also, common ratio [ common ratio will be same for each term in G.P.]
So, for , the given numbers will be in G.P.
7. Find the sum to terms the geometric progression
Hint:
Solution:
Solution step 1: The given G.P. is
So, and
By the above formula we get:
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8. Find the sum to terms in the geometric progression
Hint:
Solution:
Solution step 1: The given G.P. is
So, and
Using the above formula we get:
9. Find the sum to terms in the geometric progression
Hint:
Solution:
Solution step 1: The given G.P. is
So, first term and Common ratio
Using the above formula we get:
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10. Find the sum to terms in the geometric progression
Hint:
Solution:
Solution step 1: The given G.P. is
So, and
Using the above formula we get:
11. Evaluate
Hint:
Solution:
Solution step 1:
3, forms a G.P.
So,
Using the above formula we get:
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Putting the value in equation , we get:
12. The sum of first three terms of a G.P. is and their product is . Find the common ratio and the
terms.
Hint: Assume be the first three terms of the G.P.
Solution:
Solution step 1: Take the be the terms of the G.P.
[ By question]
[ By question]
From we get
(Taking only real root)
Putting in equation we get
or
So the 3 term of G.P. are .
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13. How many terms of G.P. are needed to give the sum 120?
Hint:
Solution:
Solution step 1: The given G.P. is
So, and
By using the above formula we get:
[ By question]
So the four terms are required to get the sum as
14. The sum of first three terms of a G.P. is 16 and the sum of the next three terms is Determine the
first term, the common ratio and the sum to terms of the G.P.
Hint: Assume the G.P, is a
Solution:
Solution step 1: Assume the G.P. be
and [ By question]
Dividing equation by we get
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Putting in ,we get:
By using the above formula we get;
15. Given a G.P. with and term , determine
Hint: and
Solution:
Solution step 1: Assume be the common ratio of the G.P.
and [ By question]
be the common ratio of the G.P.
Using the above formula we get:
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Using the above formula we get:
So the required is .
16. Find a G.P. for which sum of the first two terms is and the fifth term is times the third term.
Hint: and
Solution:
Solution step 1: Assume a be the first term and r be the common ration of A.P.
By using the above equation we get;
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From equation we get:
for
Also, for
So, the required G.P. is or
17. If the and terms of a G.P. are and , respectively. Prove that are in G.P.
Hint: and
Solution:
Solution step 1: Assume a be the first term and r be the common ration of A.P.
By using the above equation we get;
Dividing equation by , we get
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Dividing equation by , we get
So, are in G. P.
18. Find the sum to terms of the sequence,
Hint:
Solution:
Solution step 1: The given sequence is
This sequence is not a G.P. But, we can change itinto G.P. as to
terms
19. Find the sum of the products of the corresponding terms of the sequences and
Hint:
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Solution:
Solution step 1: Required sum
So the series is in G.P.
So term, and Common ratio,
By using the above equation we get;
Required sum
20. Show that the products of the corresponding terms of the sequences form
a G.P, and find the common ratio.
Hint: Common ratio
Solution:
Solution step 1: By question we get .
So the common ratio is same for all term, the series is in G.P.
21. Find four numbers forming a geometric progression which third term is greater than the first term
by , and the second term is greater than the by .
Hint:
Solution:
Solution step 1: Assume a be the first term and r be the common ration of A.P.
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By using the above formula we get:
,
[ By question]
[ By question]
From equation and we get
Dividing equation by , we get
Putting the value of in we get
So, the first four numbers of the G.P. are and i.e., and
22. If and terms of a G.P. are and , respectively. Prove that
Hint:
Solution:
Solution step 1: Assume be the first term and be the common ratio of the G.P.
By using the above equation we get:
[ By question]
[ By question]
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[ By question]
Hence proved.
23. If the first and the term of a G.P. are ad , respectively, and if is the product of terms,
prove that
Hint:
Solution:
Solution step 1: Assume the first term of the G.P is a and the last term is
Take the G.P. is , where is the common ratio.
[ By question]
Product of terms
So, is an A. P.
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Hence proved.
24. Show that the ratio of the sum of first terms of a G.P. to the sum of terms from to
term is
Hint: and Sum of first terms
Solution:
Solution step 1: Assume a be the first term and be the common ratio of the G.P.
Sum of first terms
By using the above formula we get:
Since there are terms from to term, Sum of terms from to term
So, required ratio
Hence proved.
25. If and are in G.P. show that:
Hint:
Solution:
Solution step 1: are in G.P.[by the question]
So
[by the question]
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R.H.S.
Hence proved.
26. Insert two numbers between and so that the resulting sequence is G.P.
Hint:
Solution:
Solution step 1: Assume and be two numbers between and so that the series, ,
forms a G.P.
Assume a be the first term and be the common ratio of the G.P.
(consider only real roots)
For
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So, the required two numbers are and .
27. Find the value of so that may be the geometric mean between and
Hint: Middle term of and is
Solution:
Solution step 1: G.M.
By using the above formula we get:
[ By question]
Squaring both sides, we get
So the required number n is
28. The sum of two numbers is times their geometric mean, show that number are in the ratio
Hint: Middle term of and is
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Solution:
Solution step 1: Assume the two numbers be and
G.M.
By using the above formula we get:
[ By question]
Also,
Adding and , we get:
Putting the value of a in we get:
So, the required ratio is
29. If A and be A.M. and G.M., respectively between two positive numbers, prove that the numbers
are
Hint: and
Solution:
Solution step 1: Assume two numbers be and
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From equation and , we get:
a
Substituting the value of a and from (iii) and (iv) in the (v) we get
From equation and , we get
Putting the value of a in , we get:
So the two numbers are .
30. The number of bacteria a certain culture doubles every hour. If there were bacteria present the
culture originally, how many bacteria will be present at the end of hour, hour and hour?
Hint:
Solution:
Solution step 1: Bacteria doubles every hour so the number of bacteria after every hour will form a
G.P.
So, and
Using the above formula we get:
So, the number of bacteria at the end of hour will be 120.
The number of bacteria at the end of hour will be
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So, number of bacteria at the end of hour will be
31. What will ₹ amounts to in years after its deposit in a bank which pays annual interest rate of
compounded annually?
Hint:
Solution:
Solution step 1: At the end of first year, amount ₹.
At the end of year, amount
At the end of year, amount and so on
Amount at the end of years
32. If A.M. and G.M. of roots of a quadratic equation are and respectively, then obtain the quadratic
equation.
Hint: and
Solution:
Solution step 1: Assume the root of the quadratic equation be and
Formula of quadric equation is given by:
(Sum of roots) (Product of roots)
By equation (ii) and (iii) we get:
So the quadratic equation is
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Exercise 9.4
1. Find the sum to terms of the series
Hint:
Solution:
Solution step 1: So the series is term,
2. Find the sum to terms of the series
Hint:
Solution:
Solution step 1: So the series is term,
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3. Find the sum to terms of the series
Hint:
Solution:
Solution step 1: So the series is term,
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4. Find the sum to terms of the series
Hint:
Solution:
Solution step 1: So the series is
term,
Adding the above terms we get:
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5. Find the sum to terms of the series
Hint:
Solution:
Solution step 1: So the series is term,
term is
6. Find the sum to terms of the series
Hint:
Solution:
Solution step 1: So the series is
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7. Find the sum to terms of the series
Hint:
Solution:
Solution step 1: So the series is
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8. Find the sum to terms of the series whose term is given by .
Hint:
Solution:
Solution step 1:
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9. Find the sum to terms of the series whose terms is given by
Hint:
Solution:
Solution step 1:
Take
So the above series is in G.P. where and .
By using equation (i) and (ii) we get:
10. Find the sum to terms of the series whose terms is given by
Hint:
Solution:
Solution step 1:
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Miscellaneous Exercise
1. Show that the sum of and terms of an A.P. is equal to twice the term.
Hint:
Solution:
Solution step 1: Assume be the first term and the common difference of the A.P.
By using the above formula we get:
[ By question]
So, the sum of and terms of an A.P. is equal to twice the term.
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2. If the sum of three numbers in , is 24 and their product is , find the numbers.
Hint: Assume the numbers are , and
Solution:
Solution step 1: Assume the three numbers in . be , and
[by question]
[by question]
So, when , the numbers are and and when the numbers are and
So, the three numbers are and
3. Let the sum of terms of an A.P. be and , respectively, show that
Hint:
Solution:
Solution step 1: Assume and be the first term and d is the common difference of the A.P.
By using the above formula we get:
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From equation (i) and (ii) we get:
Hence proved.
4. Find the sum of all numbers between 200 and 400 which are divisible by 7.
Hint for Overall:
Solution:
Solution Step1: The numbers lying between and which are divisible by are
First term, ,Last term, ,Common difference,
By using the above formula we get:
[By question]
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So, the required sum is 8729.
5. Find the sum of integers from to that are divisible by or
Hint:
Solution:
Solution step 1: The integers from to , which are divisible by are
So
By using the above formula we get:
By using the above formula we get:
The integers from to which are divisible by are
This forms an A.P. with both the first term and common difference equal to
By using the above formula we get:
By using the above formula we get:
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The integers, which are divisible by both and are This also forms an A.P. with both
the first term and common difference equal to
By using the above formula we get:
By using the above formula we get:
Required sum
Thus, the sum of the integers from 1 to 100, which are divisible by or is
6. Find the sum of all two-digit numbers which when divided by yields as remainder.
Hint:
Solution:
Solution step 1: The two‐digit numbers, which when divided by , yield as remainder, are
So and
Let be the number of terms of the A.P.
By using the above formula we get:
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By using the above formula we get:
So, the required sum is
7. If is a function satisfying for all , such that and
, find the value of
Hint:
Solution:
Solution step 1: By question:
for all
Taking in (1),
we take
Similarly,
that is forms a G.P.
So and .
By using the above formula we get:
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[By question]
So, the value of is .
8. The sum of some terms of G.P. is whose first term and the common ratio are and ,
respectively. Find the last term and the number of terms.
Hint:
Solution:
Solution step 1: the sum of terms of the G.P. be
It is given that the first term a is 5 and common ratio is
Last term of the G. term
So the last term of the is
9. The first term of a G.P. is 1. The sum of the third term and fifth term is . Find the common ratio of
G.P.
Hint:
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Solution:
Solution step 1: Assume abe the first term and be the common ratio of the G.P.
(consider only real roots)
So, the common ratio of the G.P. is
10. The sum of three numbers in . is . If we subtract from these numbers that order, we
obtain an arithmetic progression. Find the numbers.
Hint: Assume 3 terms of G.P. are , and
Solution:
Solution step 1: Assume the three numbers in G.P. be , and
[By question]
forms an A.P.
From equation (i) and (ii) we get
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So
So, when , the three numbers in . are and and if, , the three numbers in
. are and
Both cases the required terms are .
11. A G.P. consists of an even number of terms. If the sum of all the terms is times the sum of terms
occupying odd places, then find its common ratio.
Hint:
Solution:
Solution step 1: Let the G.P. be
Number of terms
[By question]
So the G.P. be
So, the common ratio of the G.P. is
12. The sum of the first four terms of an A.P. is . The sum of the last four terms is . If its first term
is , then find the number of terms.
Hint:
Solution:
Solution step 1: Assume the first four A.P. be
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So sum of first four terms
So sum of last four terms
[by question]
So, the number of terms of the A.P. is
13. If then show that and are in G.P.
Hint: check the given in question carefully.
Solution:
Solution step 1: [by question]
[by question]
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From equation and we get
So, and are in G.P.
14. Let be the sum, the product and the sum of reciprocals of terms in a G.P. Prove that
Hint: assume the n terms of G.P. are .
Solution:
Solution step 1: Assume the G.P. be
[By question]
[By question]
[By question]
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15. The and terms of an A.P. are respectively. Show
that
Hint:
Solution:
Solution step 1: Let be the first term and d be the common difference of the A.P.
The term of an A.P.
By using the above formula we get and .
Subtracting equation from , we get
Subtracting equation from we get
By equation (iv) and (v) we get
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Hence proved.
16. If a are in A.P., prove that are in A. P
Hint:
Solution:
Solution step 1: It is given the a are in A. P.
Thus, , and are in A.P.
17. If are in G.P, prove that are in G.P.
Hint: a, b, c will be in G.P. if .
Solution:
Solution step 1: , and are in G.P so:
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So
Taking L. H.S.
R.H.S.
Hence proved.
18. If and are the roots of and , are roots of where ,
form a G.P.
Prove that
Hint: properties of quadric equation
Solution:
Solution step 1: a and are the roots of
and [By the properties of quadric equation]
Also, and are the roots of
and [By the properties of quadric equation]
are in G.P.[by question]
Assume From and
we get
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On dividing, we get
When
When
Case I:When and
i.e.,
Case II:When
So,
So, in both the cases, we obtain 17.15
Hence proved.
19. The ratio of the A.M and G.M. of two positive numbers a and , is . Show
that
Hint: A.M and G.M.
Solution:
Solution step 1: Assume the two numbers be and
A.M and G.M.
[By question]
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Using this the identity , we get
Adding and , we get
Putting the value of a in we get
So,
20. If are in A.P; are in G.P and are in A.P. prove that are in G.P.
Hint: Common ratio in G.P. and common difference in A.P. same for each term.
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Solution:
Solution step 1: So are in A.P.
And , are in G.P.
Also, are in A.P.
We have to prove that
From equation , we get
From equation we get
Putting these values in , we get
So, , and are in G.P.
Hence proved.
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21. Find the sum of the following series up to terms:
(i) (ii)
Hint:
Solution:
Solution step 1: (i)
Take to terms
(ii)
Hint:
Solution:
Solution step 1: Take to terms
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22. Find the term of the series terms.
Hint:
Solution:
Solution step 1: The given series is terms
term
So, the term of the series is 1680.
23. Find the sum of the first terms of the series:
Hint:
Solution:
Solution step 1: The given series is
On subtracting both the equations, we get
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24. If are the sum of first natural numbers, their squares and their cubes, respectively, show
that
Hint:
Solution:
Solution step 1: By the question
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Here,
Also,
Thus, from and , we obtain
25. Find the sum of the following series up to terms:
Hint:
Solution:
Solution step 1: The term of the given series is
So, is an A.P. with first term a, last term and number of terms as
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26. Show that
Hint:
Solution:
term of the numerator
term of the denominator
Here,
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Also,
From and we get
So, the given result is proved.
27. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in
annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor
cost him?
Hint: Total interest
Solution:
Solution step 1: The farmer pays Rs 6000 in cash [By question]
Then unpaid amount According to the given condition, the interest
paid annually is
So, total interest to be paid
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Now, the series is an A.P. with both the firstterm and common difference
equal to 500.
Let the number of terms of the A.P. be
Sum of the A.P
So, total interest to be paid
of of 4680
So, cost of tractor
28. Shams had Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in
annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter
cost him?
Hint: Sum of terms of a G.P. is
Solution:
Solution step 1: Shamshad Ali buys a scooter for 22000 and pays 4000 in cash.[By question]
Unpaid amount
the interest paid annually is[By question]
10% of 18000, 10% of 17000, 10% of 16000 10% of 1000
So, total interest to be paid
of of of of 1000
of
of
Here, forms an A. P. with first term is 1000 and common difference is
1000.
So the number of terms be
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Total interest paid of
of 17100
Cost of scooter
29. A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail
to four different persons with instruction that they move the chain similarly. Assuming that the
chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage
when set of letter is mailed.
Hint: Sum of terms of a G.P. is
Solution:
Solution step 1: The numbers of letters mailed forms a
First term
Common ratio
Number of terms
Sum of terms of a G.P. is
By using the above formula
It is given that the cost to mail one letter is paisa.
Cost of mailing 87380 letters
So, the amount spent when set of letter is mailed is Rs 43690.
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30. A man deposited ₹ 10000 in a bank at the rate of 5% simple interest annually. Find the amount
in15th year since he deposited the amount and also calculate the total amount after 20 years.
Hint: Check the given in question wisely.
Solution:
Solution step 1: So the man deposited ₹ 10000 in a bank at the rate of 5%
simple interest annually.
Interest first year
Amount in15th year
Amount after 20 years
31. A manufacturer reckons that the value of a machine, which costs him , will depreciate each
year by 20%. Find the estimated value at the end of 5 years.
Hint: Use the given in question wisely.
Solution:
Solution step 1: Cost of machine
Machine depreciates by 20% every year.
Its value after every year is 80% of the original cost i.e., of the original cost.
Value at the end of 5 years
So, the value of the machine at the end of 5 years is Rs 5120.
32. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on
second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the
work. Find the number of days in which the work was completed.
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Hint:
Solution:
Solution step 1: Assume the number of days in which 150 workers finish the work is x.
terms[By question]
The series terms is an A.P.
So the first term and common difference .
We consider only positive value of x so
Originally, the number of days in which the work was completed is 17.
So required number of days