1. In a AP, fifth term and eighth terms are 10.5 and 16.5 respectively. Calculate the followinga. first termb. common differencec. sum of first eight terms

2. Fourth term of a AP is 9 and sum of first four terms is 21. Find:a. first termb. common differencec. sum of first eight terms

3. Second term of a AP is -19 and sum of fifth term and seventh term is 26. Find:a first termc. sum of first ten terms

4. In a JA, sum of the first 6 terms is 36 and sum of the first 10 terms is one third of sum of first 20 terms. Calculate:a. first termb. 10th term

5. Sum of first 5 terms in a AP is 75 and sum of first 10 terms is 200. Calculate:a. common differenceb. the least number of terms that must be added so that the total sum is not less than 500

6. In a GP, third term and sixth term is 22.5 and 607.5 respectively. Calculatea. common ratiob. first termc. sum of first 10 terms (give answer in 3 significant figures)

7. In a GP, second term exceeds the first term by 4 and the third term exceeds the second term by 16. Find:a. common ratiob. first termc. fourth term

8. In a GP, where all terms are positives, the second term is 2. It is given that the sum of fourth term and sixth term is 12. Find:a. common ratio b. tenth term

9. In a GP, the fourth term exceeds the second term by 15. Sum of the first four terms is 65. Calculate:a. common ratio (r >0)b. the corresponding first term

10. Sum of first 3 terms in a GP is 21 and sum of first six terms is 189. Calculate:a. common ratio b. the number of terms must be added so that the total sum is above 1 million

11. (a) Sum of first n terms of a AP is given as Sn = 10n + n2

calculate: i. first term ii. common difference (b) The equation Sn = 9(1 - (2/3)n ) is provided to calculate the sum of first

n terms of a GP. Calculate: i. first term ii. common ratio

12. (a) Sum of first n terms of a progression given as Sn = (3n/2) (n - 2) hence calculate the first three terms of the progression (b) Sum of n first terms of a progression is given by Sn = (5/4) (3n - 1) calculate: i. first term ii. sixth term13. The sum of a progression is given by Sn = (n/2) (n + 1)2 . Calculate the fifth

term of the progression

14. (a) Sum of first n term of a progression is given by Sn = (2n2 + 3n)/2 calculate the eighth term of the progression (b) Sum of first eight terms of a AP is 56 and the sum of first 20 terms is 260.

Calculate the first term and the common difference.

15. (a) Sum of first n term of a AP is given by Sn = (n/4) (3n + 13)Calculate first term and common difference

(b) In a different AP, the common difference is 2. The sum of first n term sis 460, while sum of first 2n terms is given as 1720. Find n and the first term.

16. (a) The first 3 terms ( all the terms is positive) of a GP is x - 2, x, 2x. Find i) x value ii) the fifth term (b) In a AP, sum of first n terms is given by Sn = 2n2 + n. Derive and simplify

the expression for Sn-1, in expression of n. Subsequently or using different method, find

i) the nth term of the progression in an expression of n ii) the first term iii) common difference

17. (a) There are 16 terms in a AP. The sum of all odd terms is 144 and sum of even terms is 136. Find

i. common difference ii. first term (b) Sum of first n terms of GP is given by Sn = 2(1 - 1(2n2)). Find

i. sum of first five terms ii. fifth term iii. sum of the terms when n approaches infinity

18. (a) Find the sum of the first 5 terms of a GP if the first term and the second term is given as 2 and 6 respectively.

The first term of a AP is 2 and the sum of the first five terms is equal to sum of first five terms of a GP stated above. Find common difference of AP.

(b) Determine whether the terms 7x, 73x, 75x is a GP or a AP. Hence determine the common difference or common ratio which ever suitable.

19. (a) The quantity 5/2, p, q, 40/81 are in a GP. Find the value p, q, and r. (b) The first term of a AP is a and the common difference is d. Obtain an

expression for sum from 10th terms to 19th terms of the AP.

20. (a) 54, x, y are three consecutive terms in a GP. Given that the sum of the three terms is 42. Find the possibly x and y values.

(b) Calculate the how many numbers are there between 100 and 300 that can be divided by 14. Calculate the sum of all the numbers.

21 (a) The terms x/2, x-4, x+2 are the three consecutive terms of a GP. Find the possible value of x and the corresponding r values.

(b) (i) Find the sum of all even integers of a number 1 to 500 (ii) Find the sum of all even integers that is not a multiple of 6 of a number

1 to 500

22. (a) If the sum of n terms of a AP given by Sn = 5n + 2, find the sum of first 20 terms of the progression

(b) A GP has a and r as the first term and common ratio respectively. It is given that the sum of the first n terms of a GP is 254, show that

arn-2 = (254(r - 1) + a)/r2

If given the first term is 2, and the nth term is 128, find r and n.

23. The nth term of an AP is Tn and the sum of first n terms is Sn. (a) For an AP, given T5 + T16 = 44, and S18 = 3S10. Calculate T1 and common

difference (b) In an another AP, T1 is 1. It is given that T7, T11, and T17 are consecutive

terms in a GP, calculate the value of each term.

24. (a) Sum of all integers from 5 to n is given by P. Sum of all integers from n + 1 to 22 is given by Q. It is given that n is located between 5 and 22, hence express P and Q in terms of n.

It is given that 2P = Q, find n value. (b) In a GP where all the terms is positive, the fifth and the seventh

terms are 20 and 5 respectively. Find (i) common ratio (ii) 8th term

(iii) first term

25. (a) It is give that Sin Φ, 2Cos Φ , and 2Sin Φ are three consecutive terms of a AP.

(i) show Tan Φ = 4/3 (ii) calculate sum of first 20 terms of the progression if Φ is acute angle (b) In a GP of 12, 18, 27 ......., calculate the minimum of terms that when added

is above 1000

26. (a) In an AP, the third term is four times the first term. Using 'a' as the first term, find the expression of sum of first n terms, in terms of 'n' and 'a'.

For a case of sum of first five terms is 45, find the fifth term (b) A circle is divided into four sectors with the sectors angles form a GP. It is

given that the largest sector angle is 8 times the size of smallest angle of sector. Find the largest angle of the sector.

27. (a) The sum of first 8 terms of a AP is 24 and sum of first 18 terms of the same AP is 90. Find the 7th term.

(b) A GP has positive common ratio and the sum of the first two terms 17(1/2) and the third term is 4(2/3). Calculate the common ratio.

28. (a) The nth term of AP is given by Un, and sum of the first n terms is given by Sn. If S10 = 3S5, find

(i) U10/U5

(ii) It is given that U5 = 0.14, find S200

(b) It is given that Cos Φ, Sin Φ , and Sin2Φ are three consecutive terms in a GP where sin Φ not equal to zero, show that

2Sin2 Φ + Sin Φ - 2 = 029. (a) In a AP, there is 20 terms. It is given that the 7th terms is 27 and the sum

of the last 7 terms is 469, calculate: (i) first term (ii) sum of the first 7 terms (b) the first term of a GP exceeds the second term by 4 and the sum of the

sum of the 2nd and third terms is 8/3. Find all possible values of first term and the corresponding common ratio.

If all the terms in GP values is positive, calculate the sum till infinity.

30. (a) In a AP, the sum of the first 30 terms is 1425 and the sum of the subsequent 30 terms is 4125. Calculate

(i) the first term and the common difference (ii) the sum of the first 2n terms (b) The first three terms of a GP is (x -3), (x + 2), and (3x - 4). Calculate (i) value of x (ii) common ratio (iii) sum of first n terms

31 (a) Two cars (Car A and Car B)move simultaneously towards each other on a straight car track. The distance between the two cars is 195m. Car A reaches a distance of 30m in the 1st second, 25m in the 2nd second, and

20m in the 3rd second and so forth. The Car B reaches a distance of 20m in the 1st second, 18m in the 2nd second, 16m in the 3rd second, and so forth. Calculate the time taken for two car to meet each other. (b) Find x for a GP of 8, x, 9. It is also given that 8 < x < 9.

32. (a) In a school cross country race, a long distance athletic took 4 minutes 20 seconds to complete the first kilometer and his speed reduces consistently in such a manner that all subsequent kilometer, he took 20 seconds extra from the previous kilometer. Find

(i) time take for the first 8 kilometers (ii) time taken to complete first 10 kilometers (b) 3p + q, 7p + q, 19p + q are the first three terms of a GP, where p ≠ 0. Find (i) q in p term (ii) common ratio

33. (a) In a AP, common difference is 4. It is given that sum of first 10 terms is equal to sum of 5 subsequent 5 terms. Find

(i) first term (ii) sum of first 15 terms (b) Each year, the price product 'A' increases by 20% of the initial price at the

beginning of the year. It is given that the price of the product 'A' is RM800 at the beginning of a year.

(i) find expression of the product price after n years in n term. (ii) find the price after 10 years

34. (a) The fifth term of a AP is 5 and sum of the first 5 terms is -55. Find, (i) common difference (ii) the number of terms that must be added so that the total sum is a

positive value (b) In a GP, the common ratio is 1/2. It's given that sum of terms till infinity is

32, calculate (i) first term (ii) sum of first five terms (iii) sum of three consecutive terms beginning with term k, express it in k.

35. (a) In a AP, the 7th term and the 17th is 7 and -73 respectively. Find (i) common difference (ii) the term with value -25 (iii) sum of terms from 7th to 17th. (b) In a GP, the first term is 81 and the common ratio is (1/2)(k - 6/k)

whereby k > 0. (i) If k = 3, find sum to infinity (ii) if k = 4, find the number of terms to be added so that the sum is more

than 16200.

36. (a) In a AP, the first term is 2, and the common ratio is d, where d > 0. The 2nd term and 7th term is x and y respectively. Express x and y in term of d. It is given that x, 10, and y are three first terms of a GP, find

(i) x and y values (ii) sum of first five terms (b) A recurring decimal is given as 0.111111...., calculate the decimal in

simplest fraction

37. (a)

The diagram shows blocks of cement placed end to end on a straight line to form a narrow road. The blocks are arranged in certain order of size and length to form GP. It's given that the smallest block is 0.8 m length and the largest block is 1.18m length. The difference in length between two consecutive blocks is 0.02m. Calculate

(i) total number of blocks used to form the straight line (ii) the total length of the narrow road (b) Calculate the fraction for the recurring decimal of 0.055555 38. (a) In a AP, the first term is a and the common difference is d. It's given that

the sum of 3rd term and 4th term is six times of first term. Form expression for

(i) d in terms of a (ii) sum of first n terms , in terms of a and n

It's given that sum of first 5 terms is 65. (iii) find the 5th term (b) The diagram shows vertical surface projections of a rubber ball from a

point O on a flat land. The ball reaches a maximum height before hit the ground on a point P1. It bounces back at P1 to repeat the process. It's given OP1 = 3m. The time taken for the first projection is T seconds. The ball will continue hitting the ground at P1, P3, P4...,with distance between P1 P2 = 3k, P2 P3= 3k2, P3 P4= 3k3....with time taken in seconds given by kT, k2T, k3T...

It's given Rn represents total distance travelled by the ball from point O to point where the ball hit the ground on the nth instance. Tn, represents total time in seconds taken for the ball to hit the ground on the nth

0.8 m 1.18 m

P4P3P2P1 3k33 k23k3 m

instance. Express Rn and Tn each as a progression in terms of k. Subsequently, given k = 3/4,

(i) show that total distance the ball travelled from point O to point it stopped moving is 12 m

(ii) find total time taken, T when the ball stopped moving

39. (a) A cloth is divided into 20 pieces. Area of each piece forms a AP. It's given that sum of areas of 3 smallest pieces is 84cm2 and the sum of areas of 2 largest pieces is 196 cm2. Find the area of the cloth before it was divided into pieces.(b) It's given that 2Sinα, 2, 8Cosα form a GP with Sinα≠0 and Cosα≠0. Show Sinα= 1/2. Subsequently find values of α for 00 < α < 3600.

40.

(a) The diagram (A) shows three squares with the length of the sizes reduces by 1 unit consecutively. The diagram (B) shows three rectangles with fixed width and the length reduces by 1 unit consecutively. Show that the areas of the rectangles form AP while the areas of squares does not form AP.

(b)

The diagram shows circles with common centre and the radius increases by d cm in an order. It's given the radius of smallest circle is 1cm and total length of circumference of the first five circles is 20πcm. Calculate d in cm.

41 (a) In a AP, the 5th term is 35, and 10th term is 95. Find (i) first term and common difference (ii) sum of first 15 terms (iii) determine whether 195 is a term in the AP (b) In a another AP, the first term is a and the common difference is d. It's given that sum of first 21 terms is 9 times greater than sum of first 5 terms. Show a = 5d. It's given that he fifth term is 0.18, find (i) value of a (ii) 10th term