The sums of first `n` terms of two A.P. `' s` are in hte ratio `(7n+2):(n+4)dot` Find the ratio of their `5t h` terms.

Explanation

To solve the problem, we need to find the ratio of the fifth terms of two arithmetic progressions (APs) given that the sums of their first n terms are in the ratio \( (7n + 2):(n + 4) \).

### Step-by-Step Solution:

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