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

Jul 31, 2017

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 ${a}_{2} / {a}_{1} = \frac{1}{5} = 0.2 , {a}_{3} / {a}_{2} = \frac{0.2}{1} = 0.2$ ,

${a}_{4} / {a}_{3} = \frac{0.04}{0.2} = 0.2$ . This constant $\left(0.2\right)$ is called common

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