Pattern Recognition - How to solve this problem? A general term of the sequence
$$
-8,-7,-10,-1,-28,53,\ldots
$$
can be expressed as $\dfrac{a-b^{n-1}}{4}$, where $a$ and $b$ are integers.
What is the value of $ab$?
Teach me how to solve this problem.

If we call this sequence $x_n$, then $a-4x_n$ is the geometric sequence $b^{n-1}$. So the first element should be $1$, meaning $a-4(-8)=1$, and the second element should be $b$, so $b=a-4(-7)$.
