SOLUTION: Three positive numbers form a geometric sequence. If the geometric mean of the first two numbers is 6 and the geometric mean of the last two numbers is 24, find the three numbers a

Algebra ->  Equations -> SOLUTION: Three positive numbers form a geometric sequence. If the geometric mean of the first two numbers is 6 and the geometric mean of the last two numbers is 24, find the three numbers a      Log On


   

Question 1039237: Three positive numbers form a geometric sequence. If the geometric mean of the first two numbers is 6 and the geometric mean of the last two numbers is 24, find the three numbers and their common ratio.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let A, B, C be the numbers.
==> sqrt%28AB%29+=+sqrt%28A%2AAr%29+=+sqrt%28A%5E2%2Ar%29+=+A%2Asqrt%28r%29=6, and
sqrt%28BC%29+=+sqrt%28Ar%2AAr%5E2%29+=+sqrt%28A%5E2%2Ar%5E3%29+=+A%2Asqrt%28r%5E3%29=24.
==> %28A%2Asqrt%28r%5E3%29%29%2F%28A%2Asqrt%28r%29%29=+r+=+24%2F6+=+4
==> A%2Asqrt%284%29+=+6 ==> highlight%28A+=+3%29.
==> B+=+3%2A4+=+highlight%2812%29,
==> C+=+12%2A4+=+highlight%2848%29.