Probability
# Linear Recurrence Relations

Let $\{x_n\}$ be the sequence $1, 5, 9, 13, \ldots.$

If $\{x_n\}$ can be defined as the recurrence relation $x_7 = a, \quad x_{n+1} = x_n + b,$ find the value of $a + b.$

The sequence $F$ is defined by $F_1 = 1$ and $F_n = 2F_{n-1}$ for $n \geq 2.$ What is $F_6?$