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Question

How many terms of the AP:15,13,11,....... are needed to make the sum 55?

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Solution

In the given AP:15,13,11,...
a=15, d=1315=2
Let the number of termswhose sum is 55 be n

Sn=n2[2a+(n1)]d=55
n2[2×15+(n1)×2]=55
n2[302n+2]=55
n[2n+32]=110
2n2+32n=110
2n232n+110=0
n216n+55=0
n25n11n+55=0
n(n5)11(n5)=0
(n5)(n11)=0
n=5,11
The values of n are positive so they are valid. We get the double answer because the sum of 6th to 11th terms is zero as some terms are negative and some are positive.

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