The sums of n terms of two arithmetic progressions are in the ratio `5n + 4 : 9n + 6`. Find the ratio of their `18^(t h)`terms.

Explanation

To solve the problem, we need to find the ratio of the 18th terms of two arithmetic progressions (APs) given that the sums of their n terms are in the ratio \(5n + 4 : 9n + 6\).

### Step-by-Step Solution:

1. **Understanding the Sum of n Terms of an AP**:
The sum of the first n terms \(S_n\) of an arithmetic progression can be expressed as:
\[
S_n = \frac{n}{2} \left(2a + (n-1)d\right)
...