Question

Consider the following geometric sequence

Answer 1

A geometric sequence is of the form:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number....in this case:

a(n)=-5*(-2)^(n-1)

So for your question:

b=-5 and c=-2

Answer 2

Answer:

Explicit formula for the geometric sequence is given by"

$a_n = a_1 \cdot r^{n-1}$

where

$a_1$ 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($a_1$ ) = -5

Common ratio (r) = -2

Since,

$\frac{10}{-5} = -2$,

$\frac{-20}{10} = -2$,

$\frac{40}{-20} = -2$.

Then substitute these given values in [1] we have;

$a_n =-5 \cdot (-2)^{n-1}$            .....[2]

Since, the explicit formula for the sequence above is expressed in the form

$a_n=b \cdot c^{n-1}$

On comparing with [2] we have

b = -5 and c = -2

Therefore, the value of b and c are: -5 and -2