the second term in a geometric sequence is 50. the fourth term in the same sequence is 112.5. what is the common ratio in this sequence?

Question

anonymous · Answer

a, 50, b, 112.5

50/a = b/50 = 112.5/b

use those equations above to solve for a and b, then find the common ratio

anonymous · Answer

I cant think of what will replace a and b

whpalmer4 · Answer

actually it's even simpler:

$$\frac{b}{50} = \frac{112.5}{b}$$

tkhunny · Answer

You do not need to replace "a".  It is not needed at all for this problem.

whpalmer4 · Answer

then your common ratio is just $$\frac{112.5}{b}$$ or $$\frac{b}{50}$$

anonymous · Answer

is there a process to get b?

whpalmer4 · Answer

or better yet, $$50*a*a=112.5$$where $a$ is your common ratio

whpalmer4 · Answer

cross multiply and solve for $b$ if you're going with the $$\frac{b}{50}=\frac{112.5}{b}$$formulation.
$$b*b = 50*112.5$$

anonymous · Answer

i got 75 and the ratio came to be 1.5... i guess that's right

tkhunny · Answer

Prove IT!!!

a = 1st term
r = common ratio

ar = 2nd term = 50
ar^2 = 3rd term
ar^3 = 4th term = 112.5

There you go!  Now, solve for r.

ar = 2nd term = 50 ==> a = 50/r
ar^2 = 3rd term
ar^3 = 4th term = 112.5 ==> a = 112.5/(r^3)

50/r = 112.5/(r^3)