AHSME 1999 Problem 20

The sequence $a_{1},a_{2},a_{3},\ldots$ satisfies $a_{1} = 19,a_{9} = 99$, and, for all $n\geq 3$, $a_{n}$ is the arithmetic mean of the first $n - 1$ terms. Find $a_2$. $\textrm{(A)} \ 29 \textrm{(B)} \ 59 \textrm{(C)} \ 79 \textrm{(D)} \ 99 \textrm{(E)} \ 179$