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Question

How many terms of the A.P. 17, 15, 13, ...... must be taken, so that their sum is 81?

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Solution

Given:
a1=17, a2=15, a3=13
Sum of n terms : Sn=81

To find n

Common difference is given by: d=anan1
Using above, d=a2a1
d=1517=2
Sum of n-terms of an AP with first terms a1 and common difference d is given by: Sn=n2(2a1+(n1)d)
81=n2[2×17+(n1)×(2)]
162=2n2+36n
n218n+81=0
(n9)2=0
n=9

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