The image presents two recurrence relations. The first recurrence relation is $a_1 = 1$, $a_{n+1} = 4a_n + 9$. The second recurrence relation is $a_1 = -1$, $a_2 = 1$, $a_{n+2} = a_{n+1} + 6a_n$.

1. Problem Description

The image presents two recurrence relations.

The first recurrence relation is $a_1 = 1$, $a_{n+1} = 4a_n + 9$.

The second recurrence relation is $a_1 = -1$, $a_2 = 1$, $a_{n+2} = a_{n+1} + 6a_n$.

2. Solution Steps

The problem does not state to solve for a specific $a_n$. Therefore, I will provide the recurrence relations as is.

First recurrence relation:

$a_1 = 1$

$a_{n+1} = 4a_n + 9$

Second recurrence relation:

$a_1 = -1$

$a_2 = 1$

$a_{n+2} = a_{n+1} + 6a_n$

3. Final Answer

First recurrence relation:

$a_1 = 1$

$a_{n+1} = 4a_n + 9$

Second recurrence relation:

$a_1 = -1$

$a_2 = 1$

$a_{n+2} = a_{n+1} + 6a_n$