<PRE><B>Question 1208236</B>
&lt;pre&gt;
Hi
David jogged for 5 days in a row. Each day he jogged 1.4km more than the day before. At the end of 5 days
he jogged a total of 20.6km. How far did he jogged on the 5th day. 

The MIDDLE day of the 5-day period is the {{{matrix(1,6, (5 + 1)/2, &quot;=&quot;, 6/2, &quot;=&quot;, 3^(rd), day)}}}
On the MIDDLE or 3&lt;sup&gt;rd&lt;/sup&gt; day, he jogged the AVERAGE/MEAN number of miles, or {{{matrix(1,4, 20.6/5, &quot;=&quot;, 4.12, miles)}}}

He jogged 4.12 miles on the 3&lt;sup&gt;rd&lt;/sup&gt; day, and consistently jogged 1.4 miles greater than previous days. 
So, &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;on the 5&lt;sup&gt;th&lt;/sup&gt; day &lt;/font&gt;&lt;/font&gt;&lt;/b&gt;(2 days after the 3&lt;sup&gt;rd&lt;/sup&gt; day), &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;he jogged&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; 4.12 + 2(1.4) = 4.12 + 2.8 = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;6.92 miles&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;.

&lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;u&gt;OR&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/u&gt;.

This is an AP/AS (Arithmetic Progression/Arithmetic Sequence) that the following SUM of an AP formula
can be used. {{{matrix(1,3, S[n], &quot;=&quot;, (n/2)(2a[1] + (n - 1)d))}}}, with: S&lt;sub&gt;n&lt;/sub&gt; = Sum of the sequence (20.6, in this case)
                                               n = Number of terms (5,in this case)
                                              a&lt;sub&gt;1&lt;/sub&gt; = The 1&lt;sup&gt;st&lt;/sup&gt; term of the sequence (UNKNOWN, in this case)
                                               d = Common difference (1.4, in this case)

          {{{matrix(1,3, 20.6, &quot;=&quot;, (5/2)(2a[1] + (5 - 1)1.4))}}} ---- Substituting 20.6 for S&lt;sub&gt;n&lt;/sub&gt;, 5 for n, and 1.4 for d
          {{{matrix(6,3, 20.6, &quot;=&quot;, (5/2)(2a[1] + (4)1.4), 20.6, &quot;=&quot;, (5/2)(2a[1] + 5.6), 20.6, &quot;=&quot;, (5/2)2(a[1] + 2.8), 20.6, &quot;=&quot;, (5/cross(2))cross(2)(a[1] + 2.8), 20.6, &quot;=&quot;, 5(a[1] + 2.8), 20.6/5, &quot;=&quot;, a[1] + 2.8)}}}
           4.12 = a&lt;sub&gt;1&lt;/sub&gt; + 2.8
     4.12 - 2.8 = a&lt;sub&gt;1&lt;/sub&gt;
           1.32 = a&lt;sub&gt;1&lt;/sub&gt; (First term of this AP/AS)

&lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;On the 5&lt;sup&gt;th&lt;/sup&gt; day, he jogged&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; 1.32 + (5 - 1)(1.4) = 1.32 + 4(1.4) = 1.32 + 5.6 = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;6.92 miles&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;.

To find the 5&lt;sup&gt;th&lt;/sup&gt; term, you could&#39;ve also used the following formula for a specific tern of an
AP/AS: {{{matrix(1,3, a[n], &quot;=&quot;, a[1] + (n - 1)d)}}}, with: a&lt;sub&gt;n&lt;/sub&gt; = a Specific tern of the sequence (UNKNOWN, in this case)
                                  n = Term Number being sought (5, in this case)
                                 a&lt;sub&gt;1&lt;/sub&gt; = The 1&lt;sup&gt;st&lt;/sup&gt; term of the sequence (1.32, in this case)
                                  d = This sequence&#39;s common difference (1.4, in this case)
&lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;SELAH!!&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/pre&gt;</PRE>