Sequences, Series, and the Binomial Theorem · Superchallenge problem

An arithmetic sequence $a_1, a_2, \dots$ with nonzero common difference and a geometric sequence $b_1, b_2, \dots$ satisfy $a_1 = b_1 = 1$, $a_2 = b_2$ and $a_4 = b_4$. Find $a_{10} + b_{10}$.