Given the geometric sequence where a1 = 5 and the common ratio is −3, what is the domain for n?
All integers where n ≥ 0, All integers where n ≥ 1, All integers where n ≥ 5, All integers where n ≤ 5

Solution:

In the geometric sequence a\(_1\) = a = 5

Common ratio r = - 3

We shall determine the general term of geometric sequence

a\(_n\) = ar^{_{n - 1}}

Substituting the values

a\(_n\) = 5 × (-3)^{n - 1}

This can be written as a function

f (n) = 5 (-3)^{n - 1}

Take f(1) = 5 for n = 1

We get a\(_1\) = 5

Geometric series begins from n = 1

Domain n ≥ 1

Therefore, the domain for n is all integers where n ≥ 1.

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Given the geometric sequence where a1 = 5 and the common ratio is −3, what is the domain for n?
All integers where n ≥ 0, All integers where n ≥ 1, All integers where n ≥ 5, All integers where n ≤ 5

Summary:

Given the geometric sequence where a1 = 5 and the common ratio is −3, the domain for n is all integers where n ≥ 1.