The sums of n terms of two AP's are in the ratio `(3n-13):(5n+21).` Find the ratio of their 24th terms.

Explanation

To solve the problem, we need to find the ratio of the 24th terms of two arithmetic progressions (APs) given that the sums of their n terms are in the ratio \( (3n - 13):(5n + 21) \).

### Step-by-Step Solution:

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