Algebra
# Arithmetic Progressions

Two sequences $\{ x, a_1, a_2, a_3, y \}$ and $\{ x, b_1, b_2, b_3, b_4, b_5, y \}$ each form an arithmetic progression. If $x \neq y$, what is the value of

$\frac{a_2 - a_1}{b_5 - b_4} ?$

For an arithmetic progression $\{a_n\}$, the following equalities hold: $a_3 + a_5 = 36, \quad a_2 a_4 = 180.$

Find the largest $n$ such that $a_n < 100.$