<PRE><B>Question 143625</B>
write the first five terms of the sequence

T&lt;sub&gt;1&lt;/sub&gt; = 1, T&lt;sub&gt;n&lt;/sub&gt; = 2T&lt;sub&gt;n-1&lt;/sub&gt; + 2

&lt;pre&gt;&lt;font size = 4 color = &quot;indigo&quot;&gt;&lt;b&gt;

You already have T&lt;sub&gt;1&lt;/sub&gt;, so you replace n by 2, 
then by 3, then by 4, then by 5.

T&lt;sub&gt;n&lt;/sub&gt; = 2T&lt;sub&gt;n-1&lt;/sub&gt; + 2

Replacing n by 2:

T&lt;sub&gt;2&lt;/sub&gt; = 2T&lt;sub&gt;2-1&lt;/sub&gt;+2 = 2T&lt;sub&gt;1&lt;/sub&gt;+2 = 2(1)+2 = 2+2 = 4

Replacing n by 3:

T&lt;sub&gt;3&lt;/sub&gt; = 2T&lt;sub&gt;3-1&lt;/sub&gt;+2 = 2T&lt;sub&gt;2&lt;/sub&gt;+2 = 2(4)+2 = 8+2 = 10

Replacing n by 4:

T&lt;sub&gt;4&lt;/sub&gt; = 2T&lt;sub&gt;4-1&lt;/sub&gt;+2 = 2T&lt;sub&gt;3&lt;/sub&gt;+2 = 2(10)+2 = 20+2 = 22

Replacing n by 5:

T&lt;sub&gt;5&lt;/sub&gt; = 2T&lt;sub&gt;5-1&lt;/sub&gt;+2 = 2T&lt;sub&gt;4&lt;/sub&gt;+2 = 2(22)+2 = 44+2 = 46

and the sequence is

T&lt;sub&gt;1&lt;/sub&gt;, T&lt;sub&gt;2&lt;/sub&gt;, T&lt;sub&gt;3&lt;/sub&gt;, T&lt;sub&gt;4&lt;/sub&gt;, T&lt;sub&gt;5&lt;/sub&gt;

or  1, 4, 10, 22, 46

Edwin&lt;/pre&gt;
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