# How do you find the next two terms of the geometric sequence 5/2, 5/3, 10/9, ...?

Nov 9, 2016

$\frac{20}{27} , \frac{40}{81}$

#### Explanation:

In a GP the next term is obtained by multiplying by $r$, the common ratio,

Find $r \rightarrow r = {T}_{3} / {T}_{2} = {T}_{2} / {T}_{1}$

$r = \frac{5}{3} \div \frac{5}{2} = \frac{5}{3} \times \frac{2}{5} = \frac{2}{3}$

Check: $\frac{5}{3} \times \frac{2}{3} = \frac{10}{9}$

${T}_{4} = \frac{10}{9} \times \frac{2}{3} = \frac{20}{27}$

${T}_{5} = \frac{20}{27} \times \frac{2}{3} = \frac{40}{81}$