Question

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

• A. 1720
• B. 1600
• C. 1680
• D. 1640

Answer 1

The correct option is C

1680

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

$a_2$ = 2 and $a_7$ = 22

a + d = 2 and a + 6d = 22

Solving these two equations, we get

a = – 2 and d = 4.

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

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

= 15 (–4 + 116)

= 15 $\times$ 112

= 1680

Hence, the sum of first 30 terms is 1680.