Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain. n an 1 −4 2 20 3 −100 an = −5(−4)n − 1 where n ≥ 1 an = −4(−5)n − 1 where n ≥ 1 an = −4(5)n − 1 where n ≥ −4 an = 5(−4)n − 1 where n ≥ −4

This question is solved using geometric sequence concepts, and doing this, we get that the correct option is:

, second option

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is the same, called common ration, and the general equation is given by:

In which is the first term and q is the common ratio.

-------------------------------------------------------

n an

1 −4

2 20

3 −100

First term is -4, so , then:

The common ratio is:

Thus:

is the sequence.

A similar example is given at link

B

Step-by-step explanation:

given the first 3 terms of the geometric sequence - 4, 20, - 100

with r = = = - 5

the n th term formula ( explicit formula ) is

=

here r = - 5 and = - 4, hence

= - 4 with n ≥ 1

x-3y=4

step-by-step e