what are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of -8

Question

danjs · Answer

you know what a geometric sequence means?

jrafferty07 · Answer

I used to, But have since forgotten.

danjs · Answer

A geometric sequence is defined as a sequence in which the quotient of any two consecutive terms is a constant

each next term is multiplied by this constant number

danjs · Answer

This makes an exponential equation , the initial starting value A when term number x=0...and common multiple b

$$\large y=A*b^x$$

danjs · Answer

The nth term in the sequence , say a(n) will be

$$a _{n}=A*b^{n-1}$$

jrafferty07 · Answer

So the equation might look like a2=4*-2^2-1?

mathmale · Answer

Another perspective related to geometric progressions:  You are looking for the "common ratio" between terms.  Each time you create a new term, you multiply the previous one by the common ratio.

How did we get the second term, -8, from the first term, 4?

If r is the common ratio, then 4r=-8, and r=?

jrafferty07 · Answer

r=-2?

mathmale · Answer

Yes, your common ratio is r = -2.  What is your first term?
Look up "geometric sequences."  Determine what they look like.  Follow that format to write your own sequence for this problem.