document.write( "Question 1044745: If three geometric means are inserted between 120 and 15/2,find the third of these geometric means \n" ); document.write( "

Algebra.Com's Answer #660134 by KMST(5328) $\"\"$ $\"About$

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If $\"3\"$ geometric means are inserted between $\"120\"$ and $\"15%2F2\"$ , those five numbers form a geometric sequence.
\n" ); document.write( "Also, all five terms are positive, meaning that so is the common ratio.
\n" ); document.write( "If

, $\"b%5B2%5D=120%2Ar\"$ , $\"b%5B3%5D=120%2Ar%5E2\"$ , $\"b%5B4%5D=120%2Ar%5E3\"$
\n" ); document.write( ", and $\"b%5B5%5D=120%2Ar%5E4=15%2F2\"$ .
\n" ); document.write( "So,
\n" ); document.write( " $\"120%2Ar%5E4=15%2F2\"$ <--> $\"r%5E4=%2815%2F2%29%281%2F120%29\"$ <--> $\"r%5E4=1%2F16\"$ <--> $\"r=1%2F2\"$
\n" ); document.write( "The thirds of those geometric means can be calculated as
\n" ); document.write( " $\"b%5B4%5D=120%2A%281%2F2%29%5E3\"$ ---> $\"b%5B4%5D=120%2F8\"$ ---> $\"b%5B4%5D=highlight%2815%29\"$ ,
\n" ); document.write( "or more easily as $\"b%5B4%5D=b%5B5%5D%281%2Fr%29=%2815%2F2%29%2A2=15\"$ .
\n" ); document.write( "
\n" ); document.write( "Alternatively, we can calculate the geometric mean of $\"120\"$ and $\"15%2F2\"$ ,
\n" ); document.write( "which would be the second of the three means to be inserted, as
\n" ); document.write( " $\"sqrt%28120%2A%2815%2F2%29%29=sqrt%2860%2A15%29=sqrt%2815%2A4%2A15%29=15%2A2=30\"$ .
\n" ); document.write( "Then we can calculate the third of the three means to be inserted as the geometric mean of $\"30\"$ and $\"15%2F2\"$ ;
\n" ); document.write( " $\"sqrt%2830%2A%2815%2F2%29%29=sqrt%2815%2A15%29=15\"$ .\r
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