Question

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

Answer 1

First term in GP, a₁ = -1
common ratio , r = 7
So, nth term , Tn = -1(7)ⁿ⁻¹ = -7ⁿ⁻¹
You can also write , f(n) = -7ⁿ⁻¹

Now, what you get domain of f(n) is all natural numbers e.g., n = {1, 2, 3, ......}
so, domain for n will be all integers where n ≥ 1
Hence, option (D) is correct.

Answer 2

Answer:

The correct option is 4.

Step-by-step explanation:

Domain is the set of all possible inputs.

It is given that first term of a geometric sequence is -1 and common ratio is 7.

$a_1=-1$

$r=7$

The nth term of a geometric function is

$a_n=ar^n$

The nth term is

$a_n=-1(7)^n$

$a_n=(7)^n$

Here, n represent the number of term, which can not be negative or zero.

Therefore the domain for n is all integers where $n\geq 1$. Option 4 is correct.