The sum of `n` terms of two arithmetic progressions are in the ratio `(3n+8):(7n+15)dot` Find the ratio of their 12th terms.

Explanation

To solve the problem, we need to find the ratio of the 12th terms of two arithmetic progressions (APs) given that the sum of their n terms is in the ratio \( (3n + 8):(7n + 15) \).

### Step-by-Step Solution:

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