document.write( "Question 1102616: Find three consecutive terms of an arithmetic sequence, if the sum of the first and second terms is 30, and if the product of the first and third terms is 153. \n" ); document.write( "
Algebra.Com's Answer #717319 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First term = a-d\r\n" );
document.write( "Second term = a\r\n" );
document.write( "Third term = a+d\r\n" );
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document.write( "\"system%28%28a-d%29%2Ba=30%2C%28a-d%29%28a%2Bd%29=153%29\"\r\n" );
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document.write( "\"system%28a-d%2Ba=30%2Ca%5E2-d%5E2=153%29\"\r\n" );
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document.write( "\"system%282a-d=30%2Ca%5E2-d%5E2=153%29\"\r\n" );
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document.write( "Solve the first equation for d:\r\n" );
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document.write( "\"2a-30=d\"\r\n" );
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document.write( "Substitute 2a-30 for d in\r\n" );
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document.write( "\"a%5E2-d%5E2=153\"\r\n" );
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document.write( "\"a%5E2-%282a-30%29%5E2=153\"\r\n" );
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document.write( "\"a%5E2-%284a%5E2-120a%2B900%29=153\"\r\n" );
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document.write( "\"a%5E2-4a%5E2%2B120a-900=153\"\r\n" );
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document.write( "\"-3a%5E2%2B120a-900=153\"\r\n" );
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document.write( "Divide through by -3\r\n" );
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document.write( "\"a%5E2-40a%2B300=-51\"\r\n" );
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document.write( "Get 0 on the right:\r\n" );
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document.write( "\"a%5E2-40a%2B351=0\"\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "\"%28a-13%29%28a-27%29=0\"\r\n" );
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document.write( "a-13=0 ;  a-27=0\r\n" );
document.write( "   a=13;     a=27\r\n" );
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document.write( "Substitute each in\r\n" );
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document.write( "\"2a-30=d\"\r\n" );
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document.write( "\"2%2813%29-30=d\";   \"2%2827%29-30=d\"\r\n" );
document.write( "\"26-30=d\";   \"54-30=d\"\r\n" );
document.write( "\"-4=d\";   \"24=d\"\r\n" );
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document.write( "So one solution is\r\n" );
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document.write( "First term = a-d = 13-(-4) = 13+4 = 17\r\n" );
document.write( "Second term = a = 13\r\n" );
document.write( "Third term = a+d = 13+(-4) = 13-4 = 9\r\n" );
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document.write( "17,13,9\r\n" );
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document.write( "And the other solution is\r\n" );
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document.write( "First term = a-d = 27-(24) = 3\r\n" );
document.write( "Second term = a = 27\r\n" );
document.write( "Third term = a+d = 27+(24) = 51\r\n" );
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document.write( "3,27,51\r\n" );
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document.write( "In both cases, the sum of the first and second \r\n" );
document.write( "terms is 30, and the product of the first and \r\n" );
document.write( "third terms is 153.\r\n" );
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document.write( "Edwin
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