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      <text>8.0.19 (Periodic sequences)</text>
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      <text><![CDATA[<h3>Periodic sequences</h3>

<p>Sequences can also demonstrate different behaviours. There areexamples of sequences where certain patterns of values are repeated. Fromally we define the following.</p>
<p>The sequence \(u_1, u_2, u_3, \ldots\) is said to be <b>periodic</b> if the same terms are always repeated, e.g. 
\[ 
u_1, u_2, \ldots, u_p, u_1, u_2, \ldots, u_p, u_1, \ldots 
\]
<p>The number of terms which are repeated (\(p\)) is called the <b>period</b> of the sequence. Considering our earlier example of \(u_n=(-1)^n\), the sequence repeats the values \(-1, 1\) over and over again, so it is periodic with period 2.</p>]]></text>
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