Answer:
The explicit formula for the geometric sequence is given by:
[tex]a_n = a_1 \cdot r^{n-1}[/tex]
where,
[tex]a_1[/tex] si the first term
r is the common ratio of the terms.
As per the statement:
Consider 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] and so on...
Substitute the given values in [1] we have;
[tex]a_n = -5 \cdot (-2)^{n-1}[/tex] where, n is the number of term.
On comparing the equation [tex]a_n = -5 \cdot (-2)^{n-1}[/tex] with [tex]a_n = b \cdot c^{n-1}[/tex] we get;
b = -5 and c = -2
Therefore, the values of b and c are:
b = -5 and c = -2
