The first three terms of a geometric progression are: (the square root
of 5), (the cubed root of 5), (the sixth root of 5).  What is the
fourth term? (show work)

Hi!!


See the following definition:
A Geometric progression is a sequence in which each term is multiplied
by a common factor r in order to obtain the following term.

We can conclude that:
(n+1)-th term / n-th term = r

In effect by definition is 
(n+1)-th term = n-th term * r

In this problem:
Initial term = 5^(1/2)
Second term  = 5^(1/3)
Third term   = 5^(1/6)

Then:

Second term / First term = r

Then:
r = 5^(1/3) / 5^(1/2) =
  = 5^(1/3 - 1/2) =
  = 5^(-1/6)

Then:
Fourth term = 5^(1/6)*5^(-1/6) =
            = 5^(1/6 - 1/6) =
            = 5^0 =
            = 1

The fourth term is 1.


I hope this helps you.

Regards.
livioflores-ga

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Clarification of Answer by livioflores-ga on 03 May 2004 01:41 PDT

A little modification to the definition:
A Geometric progression is a sequence in which, given an initial term,
each term is multiplied by a common factor r in order to obtain the
following term.

See the following page at ThinkQuest Library for more references:
"Geometric Progression"
http://library.thinkquest.org/10030/11snsgp.htm