MathNet 2009-part-05 — 172 problems (EN–VI) Question 87

If $a$, $b$, $x$, and $y$ are real numbers such that $a x + b y = 3$, $a x^{2} + b y^{2} = 7$, $a x^{3} + b y^{3} = 16$, and $a x^{4} + b y^{4} = 42$, find $a x^{5} + b y^{5}$.