Seemingly easy!!

Algebra Level 3

Let \(a,b,c\) be positive integers such that \(\frac{b}{a}\) is an integer. If \(a,b,c\) are in geometric progression and the arithmetic mean of \(a,b,c\) is \(b+2,\) find the value of

\[\dfrac{a^2+a-14}{a+1}.\]