It's Somewhat Tricky!

Algebra Level 4

Let \(a, b, c\) are positive integers such that \(\dfrac{b}{a}\) is an integer. If \(a, b, c\) are in geometric progression and the arithmetic mean of \(a, b, c\) is \(b+2\), then find the value of \(\dfrac{a^{2} + a - 14}{a + 1}\).

This is a previous year IIT - JEE Question.
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