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

Answer:

D

Step-by-step 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