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: Required explicit equation is
`f(x)=4(-3)^(x-1)`

Explanation:

Since we have given that

First term =a = 4

Second term = -12

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

So, Explicit equation would be

`f(x)=ar^(x-1)\\\\f(x)=4(-3)^(x-1)`

Hence, required explicit equation is
`f(x)=4(-3)^(x-1)`

Answer 2

Explicit formula is:

aₙ = 4(-3)ⁿ⁻¹

The domain of the above formula is:

-∞<n<∞

Explanation:

The explicit equation can be found by using the formula

aₙ = a₁ (r)ⁿ⁻¹

Where

a₁ is the first term and

r is the common ratio

We are given a₁ = 4 and a₂ = -12

r = -12/4 = -3

So, explicit formula is:

aₙ = 4(-3)ⁿ⁻¹

The domain of the above formula is:

-∞<n<∞