Answer
$10$
Work Step by Step
We have
$$ \lim\limits_{n \to \infty}{a_n}=\lim\limits_{n \to \infty} 10+(-1/9)^n=10.$$
Where we used the fact that $\lim_{x\to \infty} a^x=0$ when $|a|\lt 1$. Using Theorem 1, we get that the sequence $a_n$ converges to $10$.
