<PRE><B>Question 612425</B>
&lt;pre&gt;
The formula to learn for the nth term of arithmetic
sequences is:

a&lt;sub&gt;n&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (n-1)·d
I&#39;ll work the second one.  But I&#39;ll just give you the answer 
to the first one, so you&#39;ll have to do it by yourself, but 
you do it exactly like the second one. 

The answer to the first one is

a&lt;sub&gt;n&lt;/sub&gt; = 8n - 59 

---------------------
&lt;pre&gt;
2. a6=-31; a14=-135
&lt;pre&gt;
a&lt;sub&gt;n&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (n-1)·d


Substitute n=6

a&lt;sub&gt;6&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (6-1)d
-31 = a&lt;sub&gt;1&lt;/sub&gt; + 5d

Substitute n=14

a&lt;sub&gt;14&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (14-1)d
-135 = a&lt;sub&gt;1&lt;/sub&gt; + (13)d
-135 = a&lt;sub&gt;1&lt;/sub&gt; + 13d


So we have the system of equations:

-135 = a&lt;sub&gt;1&lt;/sub&gt; + 13d
 -31 = a&lt;sub&gt;1&lt;/sub&gt; +  5d
Multiply the second equation through by -1

-135 =  a&lt;sub&gt;1&lt;/sub&gt; + 13d
  31 = -a&lt;sub&gt;1&lt;/sub&gt; -  5d

Add those two equations:

-135 =  a&lt;sub&gt;1&lt;/sub&gt; + 13d
  31 = -a&lt;sub&gt;1&lt;/sub&gt; -  5d
-----------------

-104 =       8d

{{{(-104)/8}}} = d
{{{-13}}} = d


Substituting that in

 -31 = a&lt;sub&gt;1&lt;/sub&gt; + 5d
 -31 = a&lt;sub&gt;1&lt;/sub&gt; + 5(-13)
 -31 = a&lt;sub&gt;1&lt;/sub&gt; - 65
  34 = a&lt;sub&gt;1&lt;/sub&gt; 

So 

a&lt;sub&gt;n&lt;/sub&gt; = a&lt;sub&gt;1&lt;/sub&gt; + (n-1)·d

becomes

a&lt;sub&gt;n&lt;/sub&gt; = 34 + (n-1)·(-13)

a&lt;sub&gt;n&lt;/sub&gt; = 34 - 13(n-1)

a&lt;sub&gt;n&lt;/sub&gt; = 34 - 13n + 13

a&lt;sub&gt;n&lt;/sub&gt; = 47 - 13n

Edwin&lt;/pre&gt;
</PRE>