IKMC 2018 - Grades 9-10 - Set 2 - Self-study Question 23

Points $A_0,A_1,A_2,\ldots$ lie on a line, $A_0A_1=1$, and $A_n$ is the midpoint of $A_{n+1}A_{n+2}$ for every nonnegative integer n. Find $A_0A_{11}$.