Question

What is the next term in this geometric sequence5/6,5/9,10/27,20/81

Answer 1

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

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

Answer 2

$a_1=\frac{5}{6};\ a_2=\frac{5}{9};\ a_3=\frac{10}{27};\ a_4=\frac{20}{81}\\\\\\q=a_2:a_1\\\\q=\frac{5}{9}:\frac{5}{6}=\frac{5}{9}\cdot\frac{6}{5}=\frac{2}{3}\\\\\\a_5=a_4\cdot q\\\\a_5=\frac{20}{81}\cdot\frac{2}{3}=\frac{40}{243}\to answer$