Question

find $a_4$.$a_1 = 1LXB0a_n = 2a_{n - 1} + a_{n - 2}$write your answer as an integer or fraction in simplest form.$a_4 = \square$

Explanation:

Step1: Find $a_3$ using recurrence

Substitute $n=3$ into $a_n=2a_{n-1}+a_{n-2}$:
$a_3 = 2a_2 + a_1 = 2(-2) + 1$

Step2: Calculate value of $a_3$

$a_3 = -4 + 1 = -3$

Step3: Find $a_4$ using recurrence

Substitute $n=4$ into $a_n=2a_{n-1}+a_{n-2}$:
$a_4 = 2a_3 + a_2 = 2(-3) + (-2)$

Step4: Calculate value of $a_4$

$a_4 = -6 - 2 = -8$

Answer:

$-8$