Question

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

Answer 1

`r = 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: `" "r =5/15 = 15/45 = 45/135 = 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 `1/3`"