document.write( "Question 948183: find the value of k so that 2k+2,5k-11,7k-13 is a geometric progression \n" ); document.write( "
Algebra.Com's Answer #578689 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If we wanted to find the find the common ratio, \r\n" );
document.write( "we would divide any term by the its preceding term.\r\n" );
document.write( "Even though we don't care what the common ratio is,\r\n" );
document.write( "we use this principle as though we did want to find\r\n" );
document.write( "it:\r\n" );
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document.write( "\"matrix%281%2C3%2C%285k-11%29%2F%282k%2B2%29%2C%22%22=%22%22%2C%287k-13%29%2F%285k-11%29%29\"\r\n" );
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document.write( "Creoss-multiply:\r\n" );
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document.write( "\"5k-11%29%285k-11%29\"\"%22%22=%22%22\"\"%287k-13%29%282k%2B2%29\"\r\n" );
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document.write( "Use FOIL:\r\n" );
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document.write( "\"25k%5E2-55k-55k%2B121\"\"%22%22=%22%22\"\"14k%5E2%2B14k-26k-26\"\r\n" );
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document.write( "\"25k%5E2-110k%2B121\"\"%22%22=%22%22\"\"14k%5E2-12k-26\"\r\n" );
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document.write( "\"11k%5E2-98k%2B147\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "Factor\r\n" );
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document.write( "\"11k-21%29%28k-7%29\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "\"11k-21=0\";     \"k-7=0\"\r\n" );
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document.write( "\"11k=21\";       \"k=7\"\r\n" );
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document.write( "\"k=21%2F11\"\r\n" );
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document.write( "Those are the two possible values for k.\r\n" );
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document.write( "If we wanted to find the three terms and the common ratio r,\r\n" );
document.write( "we would substitute those values for k and find:\r\n" );
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document.write( "If k = 21/11, then the three terms would be 64/11, -16/11, 4/11,\r\n" );
document.write( "with a common ratio r = -1/4\r\n" );
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document.write( "If k = 7, then the three terms would be 16, 24, 36,\r\n" );
document.write( "with a common ratio r = 3/2  \r\n" );
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document.write( "Edwin

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