Question 40
Let $f$ be a quadratic polynomial with real coefficients, and let $g_{1}$, $g_{2}$, $g_{3}$, ... be a geometric progression of real numbers. Define $a_{n} = f(n) + g_{n}$. Given that $a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$, and $a_{5}$ are equal to $1$, $2$, $3$, $14$, and $16$, respectively, compute $\frac{g_{2}}{g_{1}}$.