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.

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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

true

step-by-step explanation:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!