Question

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

Answer 1

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.

Answer 2

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