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

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

Let a1, a2, and d1, d2 be the first terms and the common difference of the first and
second arithmetic progression respectively.
According to the given condition,