Question

The sum of the first twenty terms of an A.P. is 1090 and the sum of the next twenty terms is 3090. Then, find the common difference of A.P.?
1. 4
2. 5
3. 6
4. 7

Answer 1

Correct Answer - Option 2 : 5

Given:

S_1-20 = 1090

S_21-40 = 3090

∴ S_(1-40) = 1090 + 3090 = 4180

Formula used:

S_n = n/2 × [2a + (n – 1) d]

Where, a = first term, n = nth term, d = common difference

Calculation:

S_(1-20) = 20/2 × [2a + (20 – 1) d] = 1090

⇒ 10[2a + 19d] = 1090

⇒ [2a + 19d] = 109     ----- (1)

S_(1-40) = 40/2 × [2a + (40 – 1) d] = 4180

⇒ 20[2a + 39d] = 4180

⇒ 4a + 78d = 418    ----- (2)

Multiplying equation (1) by 2 and substracting from equation (2 ), we have –

⇒ 78d – 38d = 418 – (218)

⇒ 40d = 200

⇒ d = 200/40

⇒ d = 5

∴ The common difference is 5.