Question

If you have a geometric sequence and the "r" value is negative what is the effect? Please help!

Answer 1

So, I'm not aware of anything "wrong" with a negative r.

If you just want to know what it does to the series, we can illustrate that pretty easily.

A geometric series is one where we start with a number, a, and then multiply it by a factor, r, for each subsequent term. So the series would be:

a, ar, ar^2, ar^3, etc.

If r is negative, something will happen with the signs of each term. Assume a is positive. What will the signs of each of the terms be?

Answer 2

its multiple choice:) a. the # get bigger b. the #s get smaller c. the #s alternate from positive to negative d. the #s don't change. will that help?

Answer 3

What I'm leading to is one of those choices, so that's good :P

Answer 4

kay so Im thinkin its a. but im not sure why im thinkin that!?

Answer 5

Let's say a is positive, and r is negative.

Is a*r positive or negative?

Answer 6

positve

Answer 7

What's 2* (-3)?

Answer 8

um.. well that would be -6 right?

Answer 9

Right. That was a positive number times a negative number. The result is a negative number.

So if a is positive, and r is negative, a*r is negative.

Answer 10

So if a*r is negative, what is a*r^2?

Answer 11

hold on while I solve it

Answer 12

-36?

Answer 13

No.

So, when we multiply a positive number with a positive number, we get a positive result.
When we multiply a negative number with a negative number, we get a positive result.
When we multiply a positive number and a negative number, we get a negative result.

So, when we look at the series: a, ar, ar^2, ar^3, etc
we see that the signs will alternate if r is negative.
r is negative. r^2 = r*r is positive. r^3=r^2 * r is negative. Etc.

Answer 14

wow. thanks a lot. I never would have figured it out:)