Question

find $a_4$.
$a_1 = 2$
$a_2 = 4$
$a_n = -a_{n-1} + 2a_{n-2}$
write your answer as an integer or fraction in simplest form.
$a_4 = \square$

Explanation:

Step1: Find $a_3$ using recurrence

Substitute $n=3$, $a_1=2$, $a_2=4$
$a_3 = -a_{2} + 2a_{1} = -4 + 2\times2$

Step2: Calculate value of $a_3$

$a_3 = -4 + 4 = 0$

Step3: Find $a_4$ using recurrence

Substitute $n=4$, $a_2=4$, $a_3=0$
$a_4 = -a_{3} + 2a_{2} = -0 + 2\times4$

Step4: Calculate value of $a_4$

$a_4 = 0 + 8 = 8$

Answer:

$8$