Question

What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12

Answer 1

....................................

Answer 2

Answer:
`a_n=4(-3)^(n-1)`

Domain: Set of Natural numbers.

Explanation:

The general explicit equation for the nth term of a geometric sequence is:

`a_n=a_(1)r^(n-1)`, where r is the common ratio.

Given: First term =
`a_1=4`

Second term =
`a_2=-12`

Common Ratio=
`r=(a_2)/(a_1)=(-12)/(4)=-3`

Now, the explicit equation for given geometric sequence is:

`a_n=4(-3)^(n-1)`

• The domain of the geometric sequence is always the set of natural numbers , since each term has an order which can only represent by natural number.