Question

How do you determine whether the sequence `5, 1, 0.2, 0.04,...` is geometric and if it is, what is the common ratio?

Answer 1

This is geometric progression and common raio is `0.2`

Explanation:

`5 ,1, 0.2 ,0.04 :. a_1= 5 ; a_2=1, a_3=0.2 , a_4=0.04 ....`

For Geometric progression `a_2/a_1= a_3/a_2=a_4/a_3=` constant

Here `a_2/a_1=1/5=0.2 , a_3/a_2= 0.2/1= 0.2` ,

`a_4/a_3=0.04/0.2=0.2` . This constant `(0.2)` is called common

ratio. This is geometric progression and common raio is `0.2` [Ans]