Answer:
c. [tex] \dfrac{2}{3} [/tex]
Step-by-step explanation:
Let the common ratio be r.
[tex] a_2 = \dfrac{2}{5} [/tex]
[tex] a_3 = \dfrac{2}{5}r [/tex]
[tex] a_4 = \dfrac{2}{5}r^2 [/tex]
[tex] a_5 = \dfrac{2}{5}r^3 [/tex]
We are told that [tex] a_5 = \dfrac{16}{135} [/tex].
[tex] \dfrac{2}{5}r^3 = \dfrac{16}{135}[/tex]
[tex] \dfrac{5}{2} \times \dfrac{2}{5}r^3 = \dfrac{5}{2} \times \dfrac{16}{135}[/tex]
[tex] r^3 = \dfrac{8}{27} [/tex]
[tex] r = \sqrt[3]{\dfrac{8}{27}} [/tex]
[tex] r = \dfrac{2}{3} [/tex]
Answer: c. [tex] \dfrac{2}{3} [/tex]
