Question

find $a_4$.
$a_1 = 1$
$a_2 = -5$
$a_n = -3a_{n - 2}$
write your answer as an integer or fraction in simplest form.
$a_4 = \square$

Explanation:

Step1: Identify n for $a_4$

We need $n=4$ for $a_4$.

Step2: Apply recurrence relation

Use $a_n = -3a_{n-2}$, substitute $n=4$:
$a_4 = -3a_{4-2} = -3a_2$

Step3: Substitute $a_2$ value

We know $a_2=-5$, so:
$a_4 = -3\times(-5)$

Step4: Calculate the product

$a_4 = 15$

Answer:

15