document.write( "Question 1106813: Insert three geometric means between 1/9 and 27 \n" ); document.write( "

Algebra.Com's Answer #721804 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The two given numbers are $\"1%2F9+=+3%5E%28-2%29\"$ and $\"27+=+3%5E3\"$ .

\n" ); document.write( "Are you sure you have shown the problem correctly? Inserting FOUR geometric means would be easy; inserting three is ugly.

\n" ); document.write( "To insert four geometric means, we would need to have
\n" ); document.write( " $\"27+=+%281%2F9%29%2Ar%5E5\"$
\n" ); document.write( " $\"3%5E3+=+%283%5E%28-2%29%29%2Ar%5E5\"$
\n" ); document.write( " $\"3%5E5+=+r%5E5\"$
\n" ); document.write( " $\"3+=+r\"$

\n" ); document.write( "The sequence including the four geometric means would then be
\n" ); document.write( "1/9, 1/3, 1, 3, 9, 27.

\n" ); document.write( "To insert three geometric means, we need to have
\n" ); document.write( " $\"27+=+%281%2F9%29%2Ar%5E4\"$
\n" ); document.write( " $\"3%5E3+=+%283%5E%28-2%29%29%2Ar%5E4\"$
\n" ); document.write( " $\"3%5E5+=+r%5E4\"$
\n" ); document.write( " $\"r+=+3%5E%285%2F4%29\"$
\n" ); document.write( "The sequence including only three geometric means would then be
\n" ); document.write( "3^(-2), 3^(-3/4), 3^(1/2), 3^(7/4), 3^3. \n" ); document.write( "

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