SOLUTION: Three numbers are in G. P. Their sum is 43 and their product is 216. Find the numbers in proper order

Algebra ->  Sequences-and-series -> SOLUTION: Three numbers are in G. P. Their sum is 43 and their product is 216. Find the numbers in proper order      Log On


   

Question 1140351: Three numbers are in G. P. Their sum is 43 and their product is 216. Find the numbers in
proper order
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

The three terms are a, ar and ar^2.


Their product is  a*ar*ar^2 = (ar)^3 = 216;


hence, ar = root%283%2C216%29 = 6.


Thus the middle term of the progression is ar = 6.


3 seconds to guess two other terms: 1 and 36.


So, the progression is  1, 6, 36.


The reversed order  36, 6, 1  also works.