Let a,b,c be positive integers such that `(b)/(a)` is an integer. If a,b,c are in geometric progression and the arithmetic mean of a,b,c is`b+2`, the value of `(a^(2)+a-14)/(a+1)` is

Explanation

To solve the problem, we need to find the value of \((a^2 + a - 14)/(a + 1)\) given that \(a\), \(b\), and \(c\) are positive integers in a geometric progression (GP) and that the arithmetic mean of \(a\), \(b\), and \(c\) is \(b + 2\).

### Step-by-step Solution:

1. **Understanding the Geometric Progression:**
Since \(a\), \(b\), and \(c\) are in geometric progression, we can express \(b\) and \(c\) in terms of \(a\):
\[
b = ar \quad \text{and} \quad c = ar^2
...