Let S n denote the sum of first n -terms of an arithmetic progression. If S 10 = 530 , S 5 = 140 , then S 20 - S 6 is equal to:

Step-by-step solution

We know that the sum of n terms of an arithmetic progression with its first term as a and common difference d is S n = n 2 2 a + n - 1 d . Given, S 10 = 530 ⇒ 10 2 2 a + 9 d = 530 ⇒ 2 a + 9 d = 106       … 1 And S 5 = 140 ⇒ 5 2 2 a + 4 d = 140 ⇒ 2 a + 4 d = 56       … 2 Subtracting the two equation, we get, 5 d = 50 ⇒ d = 10 On putting the value of d in the equation 2 , we get 2 a + 4 × 10 = 56 ⇒ 2 a = 16 ⇒ a = 8 . Now, S 20 -