Question

What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12?
an = 4(−3)n − 1; all integers where n ≥ 1
an = 4(−3)n − 1; all integers where n ≥ 0
an = 4(36)n − 1; all integers where n ≥ 1
an = 4(36)n − 1; all integers where n ≥ 0

Answer 1

@dan815

Answer 2

whats your thought about it?

Answer 3

Im honestly so confused

Answer 4

well, then lets start with what your material defines or what you define a geometric sequence to be ...

Answer 5

youve most likely come across arithmetic, and geometric definitions ... what do you define the geometric as?

Answer 6

When each term is multiplied by a common ratio

Answer 7

good, so, in order to get from 4 to -12, geometrically, what do we multiply by?

Answer 8

4r = -12, what does r need to be?

Answer 9

-3

Answer 10

good, so 4(-3) seems to be an important aspect of the solution, would you agree?

Answer 11

yes!

Answer 12

ok, so that narrows the options for us.

what would you consider for a good domain? take a guess.

Answer 13

ummm.. 4?

Answer 14

well that was a guess i spose, but its not even a plausible option is it

4(-3)^(n-1), its either a or b

the first term has to be 4, soo lets equate it

4 = 4(-3)^(n-1) for what value of n does this ring true? that value will have to be the start of our domian

Answer 15

1?

Answer 16

our only options are n=0 or n=1

and yes, n=1 fits the bill for us

Answer 17

okay awesome !

Answer 18

so the answer would be a? an = 4(−3)n − 1; all integers where n ≥ 1 ?

Answer 19

???