Question

Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22

Answer 1

Let a be the first term and d be the common difference of the given A.P. Then,

a₂ = 2 and a₇ = 22

⇒ a + d = 2 and a + 6d = 22

Solving these two equations, we get

a = – 2 and d = 4.

${\displaystyle S_n=\frac{n}{2}[2a+(n–1)d]}$

${\displaystyle \therefore S_{30}=\frac{30}{2}[2\times (–2)+(30–1)\times 4]}$

⇒ 15 (–4 + 116) = 15 × 112

= 1680

Hence, the sum of first 30 terms is 1680