find the two geometric means between 7 and 189?

Question

show work.

An example problem is:
a1=2.25, a5=576

an=a1(r)n-1
a5=2.25(r)5-1
576=2.25r4
256=r4
+/-4=r

Thank you so much!

Answer 1

You need to find two geometric means between two numbers, 7 and 189. It should look like this 7 __ __ 189

an=a1(r)^n-1
a4=7(r)^4-1
189=7(r)^3
27=r^3
r=3

3 is the ratio, so you multiply 7 by 3 (which equals 21), giving you the first of the two geometric means. Multiply 21 by 3 (which equals 63) to get the second of the two.

Final answer: 21, 63

Multiplying 63 by 3 givies you 189, so it is correct.

7 21 63 189

Answer 2

You and Mikey should both have put parentheses around the (n-1) for clarity. You should also put in an exponentiation sign.

Otherwise, that's the right approach.

Or you could just count off the terms -- first blank is 7r, second blank is 7r^2, 189 = 7r^3. Solve for r, which turns out to equal 3; substitute back in to get the actual terms.