It's Somewhat Tricky!

Algebra Level 4

Let a,b,ca, b, c are positive integers such that ba\dfrac{b}{a} is an integer. If a,b,ca, b, c are in geometric progression and the arithmetic mean of a,b,ca, b, c is b+2b+2, then find the value of a2+a14a+1\dfrac{a^{2} + a - 14}{a + 1}.

This is a previous year IIT - JEE Question.
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