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

Asked by  | 3rd Jan, 2012, 08:17: PM

Expert Answer:

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.

Answered by  | 4th Jan, 2012, 09:27: AM

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