Question

Which term of the AP 15, 11, 7, ... is (−13)? Also find the sum (15 + 11 + 7 + ... + (−13).

Answer 1

In the given AP, first term, a = 15 and common difference, d = (11 - 15) = -4.
Let its n^th term be -13.
Then T_n = -13
⇒ a + (n - 1)d = -13
⇒ 15 + ( n - 1​) ⨯​ (-4) = -13
⇒ 4n = 32
⇒ n = 8
Hence, the 8^th term of the given AP is -13.
∴ Required sum = $\frac{n}{2}\left(a+l\right)$
= $\frac{8}{2}\left[15+(-13)\right]=8$
Hence, the required sum is 8.