Question

if $a_1 = 8$ and $a_n = -3a_{n - 1}$ then find the value of $a_4$.

Explanation:

Step1: Find $a_2$ using $a_1$

Substitute $n=2$, $a_1=8$ into $a_n=-3a_{n-1}$
$a_2 = -3a_1 = -3\times8 = -24$

Step2: Find $a_3$ using $a_2$

Substitute $n=3$, $a_2=-24$ into $a_n=-3a_{n-1}$
$a_3 = -3a_2 = -3\times(-24) = 72$

Step3: Find $a_4$ using $a_3$

Substitute $n=4$, $a_3=72$ into $a_n=-3a_{n-1}$
$a_4 = -3a_3 = -3\times72 = -216$

Answer:

$-216$