Question

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms.

Answer 1

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

To find : the ratio of 18^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 18^th term is required of both AP’s which is \(\frac{a+17d}{A+17D}\)

Substituting n = 35 in (i) we get,

\(\frac{a+17d}{A+17D}\) = \(\frac{179}{321}\)