Question

HELP PLEASE! Im struggling

Answer 1

Answer:

c. $\dfrac{2}{3}$

Step-by-step explanation:

Let the common ratio be r.

$a_2 = \dfrac{2}{5}$

$a_3 = \dfrac{2}{5}r$

$a_4 = \dfrac{2}{5}r^2$

$a_5 = \dfrac{2}{5}r^3$

We are told that $a_5 = \dfrac{16}{135}$.

$\dfrac{2}{5}r^3 = \dfrac{16}{135}$

$\dfrac{5}{2} \times \dfrac{2}{5}r^3 = \dfrac{5}{2} \times \dfrac{16}{135}$

$r^3 = \dfrac{8}{27}$

$r = \sqrt[3]{\dfrac{8}{27}}$

$r = \dfrac{2}{3}$

Answer: c. $\dfrac{2}{3}$