Question

The sum of first n terms of two A.P.’s is in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.

Answer 1

Assuming first AP whose first term is a and common difference d 

To find : the ratio of 5 th term of a given AP 

We know that the sum of AP is given by the formula :

s = \(\frac{n}{2}\)(2a+(n-1)d)

Substituting the values in the above equation,

s₁ = \(\frac{n}{2}\)(2a+(n-1)d)

Assuming second AP whose first term is A and common difference D 

We know that the sum of AP is given by the formula :

s = \(\frac{n}{2}\)(2A+(n-1)D)

Substituting the values in the above equation,

Given,

The ratio of the 5^th term is required of both AP’s which is \(\frac{a+4d}{A+4D}\)

Substituting n = 9 in (i) we get,

\(\frac{a+4d}{A+4D}\) = \(\frac{65}{13}\) = 5