Question

Given the geometric sequence where a1 = −1 and the common ratio is 7, what is the domain for n? A. All integers B. All integers where n ≥ −1 C. All integers where n ≥ 0 D. All integers where n ≥ 1

Answer 1

D.) would be the correct answer

Answer 2

D

Explanation:

Hello, This is a geometric sequence where the first term is
`a_1=-1`.

It means that the sequence is
`(a_n)_(n\geq 1)`.

In other words, as the common ratio is 7 the sequence is defined by

`a_1=-1`

`a_(n+1)=a_n\cdot 7 \ \ \text{ for n }\geq 1`

For instance, we can estimate the first terms:

`a_1=-1\\\\a_2=7a_1=-7\\\\a_3=7a_2=-49`

And we know that we can even find a formula for the
`n^(th)` term of the sequence by:

`a_n=a_1\cdot 7^(n-1)=-7^(n-1)`

Now, to answer the question, the domain for n is all integers where
`n\geq 1`.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you