# A.P-G.P

Given that $a_1,a_2,a_3$ is an arithmetic progression in that order so that $a_1+a_2+a_3=15$ and $b_1,b_2,b_3$ is a geometric progression in that order so that $b_1b_2b_3=27$.

If $a_1+b_1, a_2+b_2, a_3+b_3$ are positive integers and form a geometric progression in that order, determine the maximum possible value of $a_3$.

The answer is of the form $\dfrac{a+b\sqrt{c}}{d}$, where $a$, $b$, $c$, and $d$ are positive integers and the fraction is in its simplest form and $c$ is square free. Submit the value of $a + b + c + d$.

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