MathNet 2013 Question 38

Let $\{a_n\}_{n \geq 1}$ be an arithmetic sequence and $\{g_n\}_{n \geq 1}$ be a geometric sequence such that the first four terms of $\{a_n+g_n\}$ are $0, 0, 1$, and $0$, in that order. What is the 10th term of $\{a_n+g_n\}$?