Question

What is the next term in this geometric sequence
5/6,5/9,10/27,20/81

Answer 1

(20/81) * (2/3) = 40/243;

the next term in this geometric sequence is 40/243.

Answer 2

`a_1=(5)/(6);\ a_2=(5)/(9);\ a_3=(10)/(27);\ a_4=(20)/(81)\\\\\\q=a_2:a_1\\\\q=(5)/(9):(5)/(6)=(5)/(9)\cdot(6)/(5)=(2)/(3)\\\\\\a_5=a_4\cdot q\\\\a_5=(20)/(81)\cdot(2)/(3)=(40)/(243)\to answer`