The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. find the numbers.

Explanation

To solve the problem, we need to find three numbers in a Geometric Progression (G.P.) whose sum is 14. Additionally, if the first two terms are increased by 1 and the third term is decreased by 1, the resulting numbers should form an Arithmetic Progression (A.P.).

### Step-by-Step Solution:

1. **Assume the Terms of G.P.**:
Let the three numbers in G.P. be \( a \), \( ar \), and \( ar^2 \).
- Here, \( a \) is the first term and \( r \) is the common ratio.

...