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How many terms of AP 17 15 13 11 must be added to get some 72 ?explain that answer

Posted by Praveen Kumar Mahto 5 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 4 months ago

We are given a = 17, d = -2, S_n = 72 and we have to find n.
Using S_n = 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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