See formulas and exponents for tips on entering formulas.
Consider the following recurrence relation and initial conditions.
\[
a_{k}=-2 a_{k-1}+63 a_{k-2}, k \geq 2, a_{0}=-2, a_{1}=34
\]
a. Find the characteristic equation. Use \( t \) for the variable in your characteristic equation.
\[
t^{2}+2 t-63=0
\]
b. Write the distinct root(s) of the characteristic equation in a comma separated list.
\[
7,-9
\]
c. The solution to the recurrence relation is
\[
a_{n}=\square \text { for } n \geq 0
\]
Note: The solution to the recurrence relation is worth most of your grade.
