To solve this we are going to use the formula for the nth term of a geometric sequence: [tex]a_{n}=a_{1}r^{n-1}[/tex]
where
[tex]a_{n}[/tex] is the nth term
[tex]a_{1}[/tex] is the first term
[tex]r[/tex] is the common ratio
[tex]n[/tex] is the place of the term in the sequence
Notice that we can infer for our problem that [tex]B=a_{1}[/tex] and [tex]C=r[/tex].
Now, to find our common ratio, we are going to use the formula [tex]r= \frac{a_{n}}{a_{n-1} } [/tex]
where
[tex]a_{n}[/tex] is the current term in the sequence
[tex]a_{n-1}[/tex] is the previous term in the sequence
for [tex]a_{n}=10[/tex] and [tex]a_{n-1}=-5[/tex]:
[tex]r= \frac{10}{-5} [/tex]
[tex]r=-2[/tex]
Since [tex]r=C[/tex], we can conclude that [tex]C=-2[/tex].
Notice that the first therm of our geometric sequence is -5, so [tex]a_{1}=-5[/tex]. Since [tex]B=a_{1}[/tex], we can conclude that [tex]B=-5[/tex].
We can conclude that the values of B and C in our geometric sequence are: [tex]B=-5[/tex] and [tex]C=-2[/tex].
