document.write( "Question 933333: If a,b,c,d are in H.P., prove that ab+bc+cd = 3ad \n" ); document.write( "

Algebra.Com's Answer #566991 by Edwin McCravy(20056) $\"\"$ $\"About$

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If a,b,c,d are in H.P., prove that ab+bc+cd = 3ad
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document.write( "Then the reciprocals  are in AP.\r\n" );
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document.write( "Let 2k = the common difference of the AP\r\n" );
document.write( "Let m = the mean of the four terms of the AP \r\n" );
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document.write( "[Note: m is the number half-way between the middle two terms, so 1/b is k \r\n" );
document.write( "less than m and 1/a is 2k less than 1/b or 3k less than m.  Similarly 1/c\r\n" );
document.write( "is k more than m and 1/d is 2k more than 1/c or 3k more than m.)\r\n" );
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document.write( "So , , , \r\n" );
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document.write( "and , , , \r\n" );
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