If the sum of the first 2 n terms of the arithmetic progression 2 , 5,8 , … … . is equal to the sum of the first n terms of the arithmetic progression 57 , 59 , 61 , … … … …, then the value of n is equals to

Step-by-step solution

For the AP 2,5 , 8 , … … . a = 2 , d = 3 S 2 n = 2 n 2 2 × 2 + 2 n - 1 3 = n 6 n + 1 For the AP 57 , 59,61 , … … . . a = 57 , d = 2 S n = n 2 2 × 57 + n - 1 2 = n n + 56 Now, S 2 n = S n ⇒ n 6 n + 1 = n n + 56 ⇒ 5 n = 55 ⇒ n = 11