Question

Given the geometric sequence where a1=-1 and the common ratio is 7, what is the domain for n?

Answer 1

All integers where n ≥ 1

Answer 2

The domain for n is n≥1, where n∈Z or all natural numbers.

Explanation:

The first term of a geometric sequence is
`a_1=-1` and the common ratio is 7.

The nth term of a G.P. is

`a_n=a_1r^(n-1)`

It can be written as

`f(n)=a_1r^(n-1)`

`f(n)=-1(7)^(n-1)`

`f(n)=-(7)^(n-1)`

This function is defined for all n≥1, where n∈Z.

Therefore the domain for n is n≥1, where n∈Z or all natural numbers.