# Iternation definition

• Oct 8th 2008, 01:47 AM
tkexer
Iternation definition
How do I work out an iterative definition (difference equation) for the sequences:
(i). {1, 1/4, 1/9, 1/16...}
(ii). {3, -6, 12, -24...}

Thanks.
• Oct 8th 2008, 02:03 AM
CaptainBlack
Quote:

Originally Posted by tkexer
How do I work out an iterative definition (difference equation) for the sequences:
(i). {1, 1/4, 1/9, 1/16...}
(ii). {3, -6, 12, -24...}

Thanks.

i. The $n$-the term is $1/n^2$ so:

$\frac{1}{(n+1)^2} = \frac{1}{(1+\frac{1}{\sqrt{1/n^2}})^2}$

so:

$
a_{n+1}=\frac{1}{(1+\frac{1}{\sqrt{a_n}})^2},\ \ \ a_1=1
$

RonL
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