If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.

### Solution

Let the first terms be a and a' and d and d' be their respective common differences.

To get ratio of 9^{th} terms, replacing (n–1)/2 = 8

n = 17

t9/t9' = (a + 8d)/(a' + 8d')

= 120/95

= 24/19