In an arithmetic progression containing 99 terms, the sum of all the odd numbered terms is 2550 . If the sum of all the 99 terms of the arithmetic progression is k , then k 100 is equal to

Step-by-step solution

Let the terms of AP be a , a + d , a + 2 d , … . . , a + 98 d For sum of all odd numbered terms A = a , D = 2 d , N = 50 . i.e. 50 2 2 a + 49 2 d = 2550 ⇒ a + 49 d = 2550 50 = 51 ⇒ 2 a + 98 d = 102 Sum of all 99 terms is, 99 2 2 a + 98 d = 99 2 × 102 = 99 × 51 ⇒ k = 5049 ⇒ k 100 = 50.49