# How do you determine whether the sequence 5, 15, 45, 135,... is geometric and if it is, what is the common ratio?

May 9, 2017

Common ratio is $3$

#### Explanation:

Sequence : $5 , 15 , 45 , 135 , \ldots \ldots .$

${a}_{1} = 5 , {a}_{2} = 15 , {a}_{3} = 45 , {a}_{4} = 135 , \ldots \ldots .$

${a}_{2} / {a}_{1} = \frac{15}{5} = 3 , {a}_{3} / {a}_{2} = \frac{45}{15} = 3 , {a}_{4} / {a}_{3} = \frac{135}{45} = 3 , \ldots . .$

In this sequence the ratio of each term and the previous term is

constant , so it is geometric sequnce and constant is $3$.

Common ratio is $3$ [Ans]