arithmetic progressions - problem no - 6 for class 10th maths
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Arithmetic progressions - Problem no - 6 of Arithmetic progressions for class 10th maths. Lets tute is an online learning centre. We provide quality education for all learners and 24/7 academic guidance through E-tutoring. Our Mission- Our aspiration is to be a renowned unpaid school on Web-World. Contact Us - Website - www.letstute.com YouTube - www.youtube.com/letstuteTRANSCRIPT
Chapter : Arithmetic Progressions Website: www.letstute.com Chapter : Arithmetic Progressions Website: www.letstute.com
Arithmetic Progressions
Problems based on Arithmetic Progressions
Solution:
Q) The sum of first 9 terms of an AP is 351 and the sum of its first 20 terms is 1770. Find the first term of the AP and its common difference.
Sn= [2a + (n – 1)d] n 2
S9 = [2 x a + (9 – 1)d] 9 2
78 = 2a + 8d ….(1)
351 = (2a + 8d) [ S9 = 351 given] 9 2
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
351 x = 2a + 8d 2 9
and S20 = [2a + (20 – 1)d] 20 2
177 = 2a + 19d ….(2)
Subtracting equation (1) from equation (2), we get
d = 9
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
1770 = 20[ 2a + (20 – 1)d] 2 1770 = 10 [2a +19d]
177 – 78 = [2a +19d] – [2a + 8d]
78 - 72 = 2a
Substituting the value of d in equation (1), we get
78 = 2a + 72
a = 3
Hence, the first term is 3 and the common difference is 9
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
78 = 2a + 8(9)
6 = 2a
Solution:
Q) The sum of first 10 terms of an AP is 485. If its last term is 71, find the first term and the common difference of the AP.
Let a = first term and d = common difference.
Sn = (a + l) n 2
Here, n = 10, l = 71 = a10 and S10 = 485
S10 = (a + 71) 10 2
485 = 5(a + 71) [ S10 = 485, given] ….(1) 97 = a + 71
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
∴
97 – 71 = a
a = 26
an = a + (n – 1)d a10 = 26 + (10 – 1)d [Using (1)]
71 = 26 + 9d [a10 = 71] 45 = 9d
d = 5
Hence, the first term is 26 and the common difference is 5
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
Solution:
Q)The first and last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Let a = first term and d = common difference of the AP
Here, a = 17, d = 9 and an = 350
an = a + (n – 1)d 350 = 17 + (n – 1)9 333 = 9n – 9 342 = 9n n = 38
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
Sn = (a + l) n 2
S38 = (17 + 350) 38 2
S38 = 19 (367)
S38 = 6973
Hence, there are 38 terms in the AP and their sum is 6973
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
Solution: a = first term = and d = common difference = 4 - =
Q) How many terms of the AP , 4, …. must beadded to obtain the sum 216 ?
11 3
13 3
11 3 11
3 1 3
Let the sum of ‘n’ terms be 216.
Sn = [2a + (n – 1)d]n2
216 = 2 x + (n – 1) n2
11 3
1 3
216 = + - n2
22 3
1 3
1n 3
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
216 = 7 + n2
n3
216 = + 7n 2
n2
6
1296 = 21n + n2
n2 + 21n – 1296 = 0
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
216 = 21n + n2
6
(n + 48) (n – 27) = 0
Either (n + 48) = 0 or (n – 27) = 0
n = -48 (rejected) or n = 27
Problems based on Arithmetic Progressions
Chapter : Arithmetic Progressions Website: www.letstute.com
n(n + 48) – 27(n + 48) = 0
Hence, the sum of 27 terms of the given AP is 216.
n2 + 48n – 27n 1296 = 0
n2 + 21n – 1296 = 0
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Problems based onArithmetic Progressions