Question

find $a_4$.
$a_1 = 40$
$a_n = -\frac{2}{5}a_{n - 1}$
write your answer as an integer or fraction in simplest form.
$a_4 = \square$

Explanation:

Step1: Calculate $a_2$

$a_2 = -\frac{2}{5}a_1 = -\frac{2}{5} \times 40 = -16$

Step2: Calculate $a_3$

$a_3 = -\frac{2}{5}a_2 = -\frac{2}{5} \times (-16) = \frac{32}{5}$

Step3: Calculate $a_4$

$a_4 = -\frac{2}{5}a_3 = -\frac{2}{5} \times \frac{32}{5} = -\frac{64}{25}$

Answer:

$-\frac{64}{25}$