The sum of the first three terms of an arithmetic progression is 9 and the sum of their squares is 35 . The sum of the first n terms of the series can be

Step-by-step solution

Let a - d ,   a   &   a + d are three numbers in A.P. Given, a - d + a + a + d = 9 ⇒ a = 3 and a - d 2 + a 2 + a + d 2 = 35 ⇒ 3 a 2 + 2 d 2 = 35 ⇒ d = ± 2 a = 3 ,   d = 2 ⇒ 1 , 3 , 5 , … … . . S n = n 2 2 + n - 1 2 = n 2 a = 3 ,   d = - 2 ⇒ 5 , 3 , 1 , … … . . S n = n 2 10 + n - 1 - 2 = n 5 - n + 1 = n 6 - n