HMMT 2013 A2

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