How do I find the common ratio in a geometric sequence, if it only gives me the first term and the last term?

You will also need to know the number of terms.

If you know the first term:  a

the last term:  l

and the number of terms:  n,

you can use these to find the common ration: r

by using this formula that finds the last ters:  l  =  a·r^(n-1).

Example:  The first term is 16 and the 10th term is 615.09375, what is the common ratio?

Solution:     615.09375  =  16·r^(10-1)

                 615.09375  =  16·r^(9)

Divide both sides by 16:

                 38.443359375  =  r^9

Take the ninth root of both sides ( use  r^(1/9) ):

                  38.443359375 ^ (1/9)  =  1.5  <----  Answer