# Using the geometric sequence of numbers 1, 3, 9, 27, … what is r, the ratio between 2 consecutive terms?

Mar 15, 2016

r = 3

#### Explanation:

The standard terms in a geometric sequence are

$a , a r , a {r}^{2} , a {r}^{3} , \ldots \ldots \ldots \ldots \ldots \ldots \ldots . , a {r}^{n - 1}$

r is called the common ratio and is the value that each term is multiplied by to obtain the next term in the sequence.

For any geometric sequence :

$r = {a}_{2} / {a}_{1} = {a}_{3} / {a}_{2} = \ldots \ldots \ldots \ldots . = {a}_{n} / {a}_{n - 1}$

where ${a}_{1} \text{ is 1st term " , a_2" is 2nd term " " and so on }$

For the sequence given here $r = \frac{3}{1} = \frac{9}{3} = 3$