Question

Solve the linear homogenous recurrence relation with constant coefficients:

Answer 1

\[ a_{n} = -3a_{n-1}, a_{0} = 2 \]

Answer 2

\[
a_ 1 = -3 a_ 0; \\
a_ 2 = -3 a_ 1 = (-3)^2 a_ 0 \\
a_ 3 = -3 a_ 2 = 9 a_ 1 = -27 a_ 0 = (-3)^3 a_ 0 \\
\]

Answer 3

How do you write \( a_n\) ?

Answer 4

\[
a_n = 2 (-3)^n
\]