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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

Respuesta :

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 [tex]a_n[/tex] be the nth term of the sequence, then 

[tex]a_1= 2[/tex]
[tex]a_2=2(-4)[/tex]
[tex]a_3=2(-4)(-4)=2(-4)^{2} [/tex]
[tex]a_4=2(-4)(-4)(-4)=2(-4)^{3} [/tex]
.
.
.
so clearly [tex]a_n=2(-4)^{n-1} [/tex]

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"!

Answer:

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

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