Question

The sum of first n terms of an AP is given by Sn=2n^2+3n. Find the sixteenth term of the AP

Answer 1

Sn=2n-2+3n Sixteen term is 65

Answer 2

Answer:

Step-by-step explanation:

Given :-

S(n) = 2n² + 3n

Solution :-

= S(n - 1) = 2 (n - 1)² + 3(n - 1)

= 2(n² - 2n + 1) + 3n - 3

= 2n² - 4n + 2 + 3n - 3

= 2n² - n - 1

We have, a(n) = S(n) - S(n - 1)

⇒ a(n) = 2n² + 3n - (2n² - n - 1)

⇒ a(n) = 2n² + 3n - 2n² + n + 1

⇒ a(n) = 4n + 1

⇒ a(16) = 4 × 16 + 1

⇒ a(16) = 65

Hence, the sixteenth term of the AP is 65.