document.write( "Question 958856: The product of the first and the third terms of an arithmetic sequence is 5. If all terms of the sequence are positive integers, what is the fourth term? \n" ); document.write( "
Algebra.Com's Answer #586744 by Edwin McCravy(20056)\"\" \"About 
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The product of the first and the third terms of an arithmetic sequence is 5. If
\n" ); document.write( "all terms of the sequence are positive integers, what is the fourth term?
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document.write( "\"a%5B1%5D%2Aa%5B3%5D=5\"\r\n" );
document.write( "\"a%5B3%5D=a%5B1%5D%2B%283-1%29d\"\r\n" );
document.write( "\"a%5B3%5D=a%5B1%5D%2B2d\"\r\n" );
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document.write( "\"a%5B1%5D%2Aa%5B3%5D=5\"\r\n" );
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document.write( "\"a%5B1%5D%28a%5B1%5D%2B2d%29=5\"\r\n" );
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document.write( "\"a%5B1%5D+=+%28-2d+%2B-+sqrt%284d%5E2%2B20%29%29%2F2+\"\r\n" );
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document.write( "\"a%5B1%5D+=+%28-2d+%2B-+sqrt%284%28d%5E2%2B5%29%29%29%2F2+\"\r\n" );
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document.write( "\"a%5B1%5D+=+%28-2d+%2B-+2sqrt%28d%5E2%2B5%29%29%2F2+\"\r\n" );
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document.write( "\"a%5B1%5D+=+%282%28-d+%2B-+sqrt%28d%5E2%2B5%29%29%29%2F2+\"\r\n" );
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document.write( "\"a%5B1%5D+=+-d+%2B-+sqrt%28d%5E2%2B5%29+\"\r\n" );
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document.write( "What's under the square root must be a perfect square\r\n" );
document.write( "since \"a%5B1%5D\" is a positive integer. The first\r\n" );
document.write( "perfect square greater than 5 is 9, and what's under\r\n" );
document.write( "the square root will be 9 if d=2\r\n" );
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document.write( "Substituting d=2 in\r\n" );
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document.write( "\"a%5B1%5D+=+-d+%2B-+sqrt%28d%5E2%2B5%29+\"\r\n" );
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document.write( "\"a%5B1%5D+=+-2+%2B-+sqrt%282%5E2%2B5%29+\"\r\n" );
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document.write( "\"a%5B1%5D+=+-2+%2B-+sqrt%289%29+\"\r\n" );
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document.write( "\"a%5B1%5D+=+-2+%2B-+3+\"\r\n" );
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document.write( "We must take the + since \"a%5B1%5D\" is a positive integer.\r\n" );
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document.write( "\"a%5B1%5D+=+-2+%2B+3+\"\r\n" );
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document.write( "\"a%5B1%5D+=+1+\"\r\n" );
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document.write( "Since d = 2, then the sequence is\r\n" );
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document.write( "1,3,5,7\r\n" );
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document.write( "The 4th term is 7.\r\n" );
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document.write( "Edwin
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