Question

Which term of the AP 5, 9, 13, 17, ... is 81? Also find the sum (5 + 9 + 13 + 17 + ... + 81).

Answer 1

In the given AP, first term, a = 5 and common difference, d = (9 - 5) = 4.
Let its n^th term be 81.
Then T_n = 81
⇒ a + (n - 1)d = 81
⇒ 5 + (n - 1​) ⨯​ 4 = 81
⇒ 4n = 80
⇒ n = 20
Hence, the 20^th term of the given AP is 81.

∴ Required sum = $\frac{n}{2}\left(a+l\right)$
= $\frac{20}{2}\left(5+81\right)=10\times 86=860$
Hence, the required sum is 860.