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 Post subject: how do i find the nth term of a recurring sequencePosted: Thu, 11 Oct 2007 12:09:51 UTC
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Joined: Thu, 11 Oct 2007 10:36:58 UTC
Posts: 1
Location: ghana
given the recurring sequence say Un+1 = (3Un)^(1/2) and Un = 1

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my name is george from ghana i love maths a lot and i want to know the secrets all about maths

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 Post subject: Re: how do i find the nth term of a recurring sequencePosted: Thu, 11 Oct 2007 13:17:53 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, asgeorgia!

Quote:
Given the recurring sequence: . and

Find an expression for in terms of

My first impulse is to crank out the first few terms and look for a pattern.

See the pattern?

We have 3 raised to a fractional power.
. . The denominator is a power-of-2: .
. . The numerator is one less than the denominator: .

Therefore: .

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