If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33 , then the value of n is

Step-by-step solution

Let the A.P. be a ,   A 1 ,   A 2 . . . A n ,   100 Here, common difference, d = 100 - a n + 1 Given A 1 A n = 1 7 ⇒ a + d 100 - d = 1 7       . . . i Also a + n = 33 From options, when n = 23 , a = 10   and   d = 90 24 = 15 4 from i 10 + 15 4 100 - 15 4 = 55 385 = 1 7