The ratio of sums ofn terms of two A.P'.s is (2n + 1) : (2n - 1). Prove that the ratio of their 12th terms will be 47 : 45.

Explanation

To solve the problem, we need to prove that the ratio of the 12th terms of two arithmetic progressions (APs) is 47:45 given that the ratio of their sums of n terms is (2n + 1):(2n - 1).

### 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 can be expressed as:
\[
S_n = \frac{n}{2} \left(2a + (n-1)d\right)
...