Question

The sum of n terms of an AP is given by $S_n=(3n^2+5n)$. Which of its terms is 164?
(a) 25th
(b) 26th
(c) 27th
(d) 28th

Answer 1

( c) 27^th
Given: S_n = (3n² + 5n) ...(i)
Replacing n by (n - 1) in (i), we get:
S_n-1 = 3(n - 1)² + 5(n - 1)
= 3(n² - 2n + 1) + 5n - 5
= 3n² - n - 2
∴​ T_n = (S_n - S_n-1)
​ = (3n² + 5n) - (3n² - n - 2 ) = 6n + 2
∴ n^th term, T_n = (6n + 2) ...(ii)

Now, T_n = 164
⇒ (6n + 2) = 164
⇒ 6n = 162
⇒ n = 27
Hence, the 27^th term of AP is 164.