find two arithmetic means between 64 and 118 (with work if its not too much)

Question

anonymous · Answer

is this a series?

anonymous · Answer

i think it is

whpalmer4 · Answer

You're looking for two numbers, $x,y$, such that

$$\frac{x}{64} = \frac{y}{x} = \frac{118}{y} = a$$ where $a$ is the common ratio of the geometric series.  That implies that $$x=64*a$$$$y=a*x$$$$118=a*y$$Telescoping them all together$$118=64*a*a*a$$Can you determine the value of $a$, and from that, the values of the two arithmetic means?

anonymous · Answer

thanks i actually figured out the answer but that explanation made me more sure! @whpalmer4

whpalmer4 · Answer

What did you get for your answers?

anonymous · Answer

i got 82 and 100 and the common difference is 18! @whpalmer4

whpalmer4 · Answer

Oh, sorry, you did arithmetic means, not geometric...

anonymous · Answer

oh no worries!

whpalmer4 · Answer

But, duh, that's what is asked for...I could have sworn I saw geometric!!!

whpalmer4 · Answer

Well, if you need to find geometric means, now you know how :-)