# Looks tough! [part 3]

Algebra Level 4

$\large 1 + 4x + 7x^2 + 10x^3 + \cdots = \dfrac{35}{16}$

Find the value of $$x$$ satisfying the equation above. If $$x$$ is in the form of $$\dfrac ab$$ where $$a$$ and $$b$$ are positive integers with $$\gcd(a,b)=1$$, submit your answer as $$a+b$$.

Hint: The series is an arithmetic-geometric progression.

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