document.write( "Question 1062612: The third term of an A.P. is 4 more than twice the first term.
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Algebra.Com's Answer #677571 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I have a problem with your typo \"trice\".  There is such\r\n" );
document.write( "a word in the dictionary.  However \"trice\" means \"in a \r\n" );
document.write( "moment\" or \"very quickly.\"  You could have meant \"twice\",\r\n" );
document.write( "which means \"two times\", or you could have meant \"thrice\"\r\n" );
document.write( "which means \"three times\".  I will assume you meant \"twice\".\r\n" );
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document.write( "Here are the first 8 terms:\r\n" );
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document.write( "a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d, a+7d\r\n" );
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document.write( " a+2d = 2a+4\r\n" );
document.write( "   2d = a+4\r\n" );
document.write( " 2d-4 = a\r\n" );
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\n" ); document.write( "The 8th term is 4 less than \"trice\" the third term.
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document.write( "Assuming \"trice\" means \"twice\",\r\n" );
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document.write( " a+7d = 2(a+2d)-4\r\n" );
document.write( " a+7d = 2a+4d-4\r\n" );
document.write( "   3d = a-4\r\n" );
document.write( " 3d+4 = a\r\n" );
document.write( " 3d+4 = a\r\n" );
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document.write( "and since 2d-4 = a,\r\n" );
document.write( "          2d-4 = 3d+4 \r\n" );
document.write( "            -8 = d\r\n" );
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document.write( "          2d-4 = a\r\n" );
document.write( "       2(-8)-4 = a\r\n" );
document.write( "         -16-4 = a\r\n" );
document.write( "           -20 = a    \r\n" );
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document.write( "Fifth term = a+4d = -20+4(-8) = -20-32 = -52.\r\n" );
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document.write( "That's the answer.\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "The A.P. is\r\n" );
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document.write( "a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d, a+7d\r\n" );
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document.write( "-20, -20+(-8), -20+2(-8), -20+3(-8), -20+4(-8), -20+5(-8), -20+6(-8), -20+7(-8)  \r\n" );
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document.write( "-20, -20-8, -20-16, -20-24, -20-32, -20-40, -20-48, -20-56\r\n" );
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document.write( "-20, -28, -36, -33, -52, -60, -68, -76\r\n" );
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document.write( "Checking the first sentence:\r\n" );
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document.write( "The third term of an A.P. is 4 more than twice the first term.\r\n" );
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document.write( "-36 is 4 more than twice -20.\r\n" );
document.write( "Twice -20 is -40, and 4 more is -40+4 = -36.  That checks.\r\n" );
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document.write( "Checking the second sentence:\r\n" );
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document.write( "The 8th term is 4 less than twice the third term\r\n" );
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document.write( "-76 is 4 less than twice -36\r\n" );
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document.write( "Twice -36 is -72, and 4 less than that is -72-4 = -76.\r\n" );
document.write( "That checks too, so if \"trice\" means \"twice\", then this\r\n" );
document.write( "is correct.\r\n" );
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document.write( "Edwin

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