<PRE><B>Question 827422</B>
&lt;pre&gt;
Use the formula for the nth term of an arithmetic sequence

a&lt;sub&gt;n&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (n-1)d

with n=10  

a&lt;sub&gt;10&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (10-1)d

a&lt;sub&gt;10&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + 9d

Substitute 75 for a&lt;sub&gt;10&lt;/sub&gt;

75 = a&lt;sub&gt;1&lt;/sub&gt; + 9d

75 - a&lt;sub&gt;1&lt;/sub&gt; = 9d 

Since the right side is 9d, pick a number for a&lt;sub&gt;1&lt;/sub&gt;
so that the left side will be a multiple of 9.  You don&#39;t
have to, but that&#39;s the way to avoid fractions.  If we pick
a&lt;sub&gt;1&lt;/sub&gt; to be 3, the left side will be 72 and that
is divisible by 9.

So let&#39;s pick a&lt;sub&gt;1&lt;/sub&gt; = 3

75 - 3 = 9d
    72 = 9d
     8 = d

So substitute a&lt;sub&gt;1&lt;/sub&gt; = 3 and d = 8 in

a&lt;sub&gt;n&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (n-1)d

a&lt;sub&gt;n&lt;/sub&gt; = 3 + (n-1)(8)

a&lt;sub&gt;n&lt;/sub&gt; = 3 + 8n-8

a&lt;sub&gt;n&lt;/sub&gt; = 8n - 5     &lt;-- answer

Then the sequence goes:

3,11,19,27,35,43,51,59,67,75,83,91,99,107,...

Notice that the tenth term is 75.

You could give other answers by choosing different 
numbers for a&lt;sub&gt;1&lt;/sub&gt;.

Edwin&lt;/pre&gt;</PRE>