The sum of the first n terms of an AP is (3n 2 + 6n). Find the nth term and the 15th term of this AP.

Question

Philoid · Accepted Answer

Sum of first n terms = S_n = 3n² + 6n

Now let a_n be the n^th term of the AP.

To find: a_n and a₁₅

Then a_n =S_n - S_{n - 1}

= (3n² + 6n) - (3(n - 1)² + 6(n - 1))

= (3n² + 6n) - (3n² + 3 - 6n + 6n - 6)

= 6n + 3

Now, a₁₅ = 6(15) + 3

= 93