Question

Given the geometric sequence where a1 = 5 and the common ratio is −3, what is the domain for n?

Answer 1

Domain: all integers where n ≥ 1

Explanation:

We are given that a geometric sequence has
`a_1 = 5` and the common ratio
`r=-3`.

We know that the general form of a geometric sequence is given by:

`a_n=ar^(n-1)`

Substituting the given values in it to get:

`a_n=5(-3)^(n-1)`

Now writing it as a function:

`f(n)=5(-3)^(n-1)`

`f(1)=5`

So the geometric series starts from n = 1, therefore the domain = n≥1