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 pf b and c
b=
c=

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

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,

`(10)/(-5) = -2`,

`(-20)/(10) = -2`,

`(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