Question 1149133
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<pre>

If 4 arithmetic means are inserted between 1 and 36, it means that you have an arithmetic progression with 6 terms:


    the first term is 1 and the last, 6-th term is 36.


There are 5 gaps in the number line between these 6 terms of the AP.

The gaps are of the same length, which is, hence,  {{{(35-1)/5}}} = {{{35/5}}} = 7.


Thus, the common difference is exactly the value of the gap, i.e. 7 units.


Thus the AP is  1, 8, 15, 22, 29, 36.


<U>ANSWER</U>.  n = 6, which is MORE THAN OBVIOUS.

         Common difference is 7.
</pre>

Solved.



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<U>Notice</U>.  &nbsp;The info about the sum &nbsp;(148) &nbsp;is not necessary and excessive.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is NOT USED in the solution.