Question

What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of -8

Answer 1

`\large\boxed{a_n=2(-4)^(n-1)=((-4)^n)/(2)}`

Explanation:

The explicit equation of a geometric sequence:

`a_n=a_1r^(n-1)`

The domain is the set of all Counting Numbers.

We have the first term of
`a_1=2` and the second term of
`a_2=-8`.

Calculate the common ratio r:

`r=(a_(n-1))/(a_2)\to r=(a_2)/(a_1)`

Substitute:

`r=(-8)/(2)=-4`

`a_n=(2)(-4)^(n-1)\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\a_n=(2\!\!\!\!\diagup^1)\left(((-4)^n)/(4\!\!\!\!\diagup_2)\right)\\\\a_n=((-4)^n)/(2)`

Answer 2

Explanation:

A geometric sequence has a common ratio. in this case the common ratio

r = -8/2 = -4.

The explicit formula is an = 2(-4)^(n-1).