document.write( "Question 1149133: if 4 arithmetic means are inserted between 1 & 36 the sum of the resulting terms is 148 .find the common difference and n . thank you \n" ); document.write( "

Algebra.Com's Answer #770482 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The given information is inconsistent -- i.e., self-contradictory.

\n" ); document.write( "When 4 arithmetic means are inserted between 1 and 36, the difference of 35 is divided into 5 equal intervals.

\n" ); document.write( "35/5 = 7; the common difference is 7.

\n" ); document.write( "The 4 arithmetic means are 8, 15, 22, and 29.

\n" ); document.write( "The sum of the 4 arithmetic means is 74.

\n" ); document.write( "The sum of all 6 terms is 111.

\n" ); document.write( "There is no sum of 148 anywhere....

\n" ); document.write( "Note if the number of arithmetic means is 6, then the problem is valid.

\n" ); document.write( "6 arithmetic means --> 35 is divided into 7 intervals.

\n" ); document.write( "35/7 = 5; the common difference is 5.

\n" ); document.write( "The 6 arithmetic means are 6, 11, 16, 21, 26, 31; their sum is 111.

\n" ); document.write( "The sum of the terms including the 1 and 36 is 148.
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