Question

First term of an A. P. is 17 and common difference is-2. If the sum of some terms is 72, find the numbers of terms and discuss the double answer.​

Answer 1

Answer:

n = 6 or n = 12

Step-by-step explanation:

Given: a = 17 , d = -2 , Sₙ = 72

w.k.t., Sₙ = n [2a + (n-1)d] / 2

So, Sₙ = n [2*17 + (n-1)(-2)] / 2 = 72

or n (34 - 2n + 2) = 144

or 36n - 2n² = 144

or n² - 18n + 72 = 0

or n² - 6n - 12n + 72 = 0

or n(n-6) - 12(n-6) = 0

or (n-6)(n-12) = 0

⇒ n = 6 or n = 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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