Question

The sum of the first n terms of an AP is given by S_n = (3ⁿ - n). find its

(i) nth term, 

(ii) first term and 

(iii) common difference.

Answer 1

Given: S_n = (3n² - n) ........(i)

Replacing n by (n - 1) in (i), we get:

S_n-1 = 3(n - 1)² - (n - 1)

= 3(n² - 2n + 1) - n + 1

= 3n² - 7n + 4