# Math Help - Multiple Arithmetic Means

1. ## Multiple Arithmetic Means

The question is "Find four Arithmetic means between .5 and 11.5"
I don't understand how to start the book doesn't help and had to learn by ourselves over the weekend for test tommorow.
Also "Find four geometric means between 1/5 and 1/160"

2. Basically, you're asked in the first one to make an arithmetic sequence that looks like:

0.5, ___, ___, ___, ___, 11.5

where each blank will be filled with an arithmetic mean. So, we need to cover 11 units (11.5 - 0.5) by adding the same number 5 times. This means we need to add 11/5 (or 2 1/5) each time. So add 11/5 to the first term to get your first arithmetic mean, then add 11/5 to that to get your next mean, and so on. You should end up at 11.5.

To find four geometric means, we know that we're going to have to multiply by our common ratio, a, a total of 5 times. So, we know:

$\frac{1}{5}* a^5 = \frac{1}{160}$.

Solve for a, find the common ratio, and use that to construct each of your geometric means.