Question

If the ratio of the sum of n terms of two APs is (7n + 1) : (4n + 27), then the ratio of their 11^th terms will be

(A)  2 : 3

(B)  3 : 4

(C)  4 : 3

(D)  5 : 6

Answer 1

Correct option  (C) 4 : 3

Let S_n and S'_n be the sums of n terms of two AP’s and T₁₁  and T₁₁ be the respective 11^th terms. Then

Now put n = 21. We get

Note: If ratio of sum of n terms of two APs is given in terms of n and ratio of their p^th terms is to be found then put n = 2p - 1. Here we put n = 11 x 2 - 1 = 21.