Question
Tue January 03, 2012 By:
 

How many terms of the A.P. 17,15,13,11.... must be added to get the sum 72? explain the double answer?

Expert Reply
Wed January 04, 2012

We are given a = 17, d = -2, Sn = 72 and we have to find n.
Using Sn = n[2a +(n -1)d]/2, we get
72 = n[2.17 +(n -1)(-2)]/2 = n(36 -2n)/2 = n(18 -n)
=> n² -18n +72 = 0 => (n -6)(n -12) = 0
=> n = 6, 12
Both values of n, being positive integers are valid. We get double answer because sum of 7th to 12th terms is zero, as some terms are positive and some are negative.

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