What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?
a. an=2(-8)^n-1; all integers where n> 1
b. an=2(-8)^n-1; all integers where n> 0
c. an=2(-4)^n-1; all integers where n> 0
d. an=2(-4)^n-1; all integers where n> 1

The common ratio in a geometric sequence is the ratio between 2 consecutive terms:

-8/2=-4, 

then the sequence is  2, -8, 32, -128, -512, 2048, ...

let  be the nth term of the sequence, then 





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so clearly

and, clearly n are integers >0, since we have a 1st term, a second term and so on... of a sequence (we do not have a "zero'th term"!



C. an=2(-4)^n-1; all integers where n>0