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

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

the answer will be