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

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

Answer 2

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= (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= (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`.