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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