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Given the geometric sequence where a1 = −3 and the common ratio is 9, what is the domain for n?

A) All integers
B) All integers where n ≥ −1
C) All integers where n ≥ 1
D) All integers where n ≥ 0

Respuesta :

aorischak99
i think its B) All integers where n ≥ -1
i may be wrong

Answer:

Option C - All integers , where [tex]n\geq 1[/tex]                          

Step-by-step explanation:

Given : The geometric sequence where [tex]a_1 = -3[/tex]  and the common ratio is 9,

To find : What is the domain for n?

Solution :

First we form a geometric sequence,

The nth term of geometric sequence is [tex]T_n=ar^{n-1}[/tex]

First term in GP,  [tex]a_1 = -3[/tex]

Common ratio, r = 9

Substitute the value,

[tex]T_n=ar^{n-1}[/tex]

[tex]T_n=(-3)(9)^{n-1}[/tex]

Now, what you get domain of [tex]T_n[/tex] is all natural numbers e.g., n = {1, 2, 3, ......}

so, domain for n will be all integers where n ≥ 1

Hence, option (C) is correct.

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