Question

The sum of the first n terms of the arithmetic progression is equal to half the sum of the next n terms of the same progression. Find the ratio of the sum of the first 3n terms of the progression to the sum of its first n terms. 

(a) 5 

(b) 6 

(c) 7 

(d) 8

Answer 1

Correct option (b) 6    

Explanation: 

If the sum of the first n terms is ‘x’, the sum of the next n terms is given as ‘2x’ (as defined in the problem). Naturally, the sum of the next n terms would be ‘3x’ (When you add the same number of terms of an AP consecutively, you get another AP). Thus, the required ratio is 6x/x = 6.