Consider the following geometric sequence: -5, 10, -20, if the explicit formula for the sequence above is expressed in the form an=b•c ^n-1 determine the values of b and c

To solve this we are going to use the formula for the nth term of a geometric sequence: 
where 
is the nth term 
is the first term 
is the common ratio 
is the place of the term in the sequence

Notice that we can infer for our problem that  and .

Now, to find our common ratio, we are going to use the formula 
where
is the current term in the sequence 
is the previous term in the sequence
for  and :



Since , we can conclude that .

Notice that the first therm of our geometric sequence is -5, so . Since , we can conclude that .

We can conclude that the values of B and C in our geometric sequence are:  and .