<PRE><B>Question 1149133</B>
&lt;br&gt;
The given information is inconsistent -- i.e., self-contradictory.&lt;br&gt;
When 4 arithmetic means are inserted between 1 and 36, the difference of 35 is divided into 5 equal intervals.&lt;br&gt;
35/5 = 7; the common difference is 7.&lt;br&gt;
The 4 arithmetic means are 8, 15, 22, and 29.&lt;br&gt;
The sum of the 4 arithmetic means is 74.&lt;br&gt;
The sum of all 6 terms is 111.&lt;br&gt;
There is no sum of 148 anywhere....&lt;br&gt;
Note if the number of arithmetic means is 6, then the problem is valid.&lt;br&gt;
6 arithmetic means --&gt; 35 is divided into 7 intervals.&lt;br&gt;
35/7 = 5; the common difference is 5.&lt;br&gt;
The 6 arithmetic means are 6, 11, 16, 21, 26, 31; their sum is 111.&lt;br&gt;
The sum of the terms including the 1 and 36 is 148.&lt;br&gt;

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