Question

Question 13 If the sum of n terms of an A.P. is 3n^2 + 5n and its mth term is 164, find the value of m.

Class X1 - Maths -Sequences and Series Page 185

Answer 1

Sₙ = 3n² + 5n
we know,
Tₙ = Sₙ - Sₙ_₁
= 3n² + 5n - 3(n-1)² - 5(n-1)
= 3(n² - n² + 2n -1) + 5(n -n + 1)
= 3(2n -1) + 5
= 6n - 3 + 5
= 6n + 2

hence , Tₙ = 2 + 6n

now,
Given, Tₘ = 2 + 6m = 164
2 + 6m = 164
6m = 162
m = 27

hence, m = 27