MathNet 2008-part-01 — 165 problems (EN–VI) Question 115

Let $f(x) = ax + b$, with $a, b$ real numbers; $f_1(x) = f(x)$, $f_{n+1}(x) = f(f_n(x))$, $n = 1, 2, \dots$. If $f_7(x) = 128x + 381$, then $a + b = \underline{\hspace{2cm}}$.