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

Answer:

Step-by-step 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).

Answer 2

Answer:

$\large\boxed{a_n=2(-4)^{n-1}=\dfrac{(-4)^n}{2}}$

Step-by-step 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:

$r=\dfrac{a_{n-1}}{a_2}\to r=\dfrac{a_2}{a_1}$

Substitute:

$r=\dfrac{-8}{2}=-4$

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