# How do you find the common ratio of the geometric sequence 135, 45, 15, 5?

May 19, 2017

$r = \frac{1}{3}$

#### Explanation:

To find the common ratio, $r$ of a geometric sequence, divide any term in the sequence by the one before it.

Check with at least two different pairs of terms to be sure:

$r = {T}_{4} / {T}_{3} = {T}_{3} / {T}_{2} = {T}_{2} / {T}_{1}$

You can also use this idea to form an equation if necessary.

In general: $r = {T}_{n} / {T}_{n - 1}$

In this case we have: $\text{ } r = \frac{5}{15} = \frac{15}{45} = \frac{45}{135} = \frac{1}{3}$

Remember that we ALWAYS multiply by $r$ to get from one term to the next.

So although in this case you might see the term-to term rule as
"Divide by 3", it is better to say "Multiply by $\frac{1}{3}$"