What is the common ratio of the geometric series below?
24 + (-8) + 8/3 + (-8/9) +...
I don't understand this, can someone help explain how I do this?
B. -1/3 D. 5,592,405/2 C. (cant write out its too weird :P)
So ya, its B D C
He right ^
The ratio between -8 and 24 is not -3, it's -1/3, which is correct. 24 times -1/3 is -8, -8 times -1/3 is 8/3, and so on. (It's much easier to solve these problems when you for multiplication instead of division.) If you are looking for division, then you would divide by -3: 24 divided by -3 is -8, -8 divided by -3 is 8/3, and so on (the same pattern as above).
what you do with a term to get to the next term
the ratio between two consecutive terms ... -8 / 24 = ?
ez is right
-3, but it's not the same for the jump of -8 and 8/3... that'd be -1/3
EZ is right !
Certainly! To determine the common ratio of a geometric series, we need to examine the pattern in the terms of the series.
In this case, we can observe that each term is obtained by multiplying the previous term by a specific value. Let's identify this value step by step:
1. To get from 24 to -8, we divide by -3. So, the ratio between these two terms is -8/24 = -1/3.
2. To get from -8 to 8/3, we multiply by -1/3. Therefore, the ratio between these two terms is (8/3) / (-8) = 1/3.
3. To get from 8/3 to -8/9, we multiply by -1/3. Thus, the ratio between these terms is (-8/9) / (8/3) = -1/3.
By observing this pattern, we can conclude that the common ratio between consecutive terms is always -1/3.