Answer:
Explicit formula for the geometric sequence is given by"
[tex]a_n = a_1 \cdot r^{n-1}[/tex]
where
[tex]a_1[/tex] is the first term
r is the common ratio term.
n is the number of terms.
Given the following geometric sequence
-5,10,-20,40
First term([tex]a_1[/tex] ) = -5
Common ratio (r) = -2
Since,
[tex]\frac{10}{-5} = -2[/tex],
[tex]\frac{-20}{10} = -2[/tex],
[tex]\frac{40}{-20} = -2[/tex].
Then substitute these given values in [1] we have;
[tex]a_n =-5 \cdot (-2)^{n-1}[/tex] .....[2]
Since, the explicit formula for the sequence above is expressed in the form
[tex]a_n=b \cdot c^{n-1}[/tex]
On comparing with [2] we have
b = -5 and c = -2
Therefore, the value of b and c are: -5 and -2
