Question

Consider the following geometric sequence: -5, 10, -20, 40,..... 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

Answer 1

To solve this we are going to use the formula for the nth term of a geometric sequence: $a_{n}=a_{1}r^{n-1}$
where 
$a_{n}$ is the nth term 
$a_{1}$ is the first term 
$r$ is the common ratio 
$n$ is the place of the term in the sequence

Notice that we can infer for our problem that $B=a_{1}$ and $C=r$.

Now, to find our common ratio, we are going to use the formula $r= \frac{a_{n}}{a_{n-1} }$
where
$a_{n}$ is the current term in the sequence 
$a_{n-1}$ is the previous term in the sequence
for $a_{n}=10$ and $a_{n-1}=-5$:
$r= \frac{10}{-5}$
$r=-2$

Since $r=C$, we can conclude that $C=-2$.

Notice that the first therm of our geometric sequence is -5, so $a_{1}=-5$. Since $B=a_{1}$, we can conclude that $B=-5$.

We can conclude that the values of B and C in our geometric sequence are: $B=-5$ and $C=-2$.

Answer 2

When solving the geometric sequence look for what how the sequence is set up from the number it starts with and how the sequence is developed.
b=-5
c=-2