Question

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

Answer 1

`20/27, 40/81`

Explanation:

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

Find `r rarr r = T_3/T_2 = T_2/T_1`

`r = 5/3 div 5/2 = 5/3 xx 2/5 = 2/3`

Check: `5/3 xx 2/3 = 10/9`

`T_4 = 10/9 xx 2/3 = 20/27`

`T_5 = 20/27 xx2/3 = 40/81`