document.write( "Question 987074: Use the approach in Gauss's Problem to find the following sums of arithmetic sequences (do not use formulas):\r
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Algebra.Com's Answer #607884 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Gauss's method:  (average term) × (number of terms).\r\n" );
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document.write( "1. To find the average term, add the first and last term, and divide by 2.\r\n" );
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document.write( "2. To find the number of terms, subtract first and last terms, divide by\r\n" );
document.write( "difference between terms and add 1.\r\n" );
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document.write( "a. 1+2+3+4+...+49\r\n" );
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document.write( "Average term: 1+49=50, divide by 2, get 25\r\n" );
document.write( "Number of terms: 49-1=48, 2-1=1, 48÷1=48, 48+1=49\r\n" );
document.write( "                 [Actually you could easily just tell there were 49 terms,\r\n" );
document.write( "                  but that's not as easy on the others]\r\n" );
document.write( "Average term × Number of terms = 25×49 = 1225  \r\n" );
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document.write( "b. 1+3+5+7+...+2009\r\n" );
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document.write( "Average term: 1+2009=2010, divide by 2, get 1005\r\n" );
document.write( "Number of terms: 2009-1=2008, 3-1=2, 2008÷2=1004, 1004+1=1005 terms\r\n" );
document.write( "Average term × Number of terms = 1005×1005 = 1010025 \r\n" );
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document.write( "c. 6+12+18+...+600\r\n" );
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document.write( "Average term: 6+600=606, divide by 2, get 303\r\n" );
document.write( "Number of terms: 600-6=594, 12-6=6, 594÷6=99, 99+1=100 terms\r\n" );
document.write( "Average term × Number of terms = 303×100 = 30300 \r\n" );
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document.write( "d. 1000+995+990+...+5\r\n" );
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document.write( "Average term: 1000+5=1005, divide by 2, get 502.5\r\n" );
document.write( "Number of terms: 1000-5=995, 1000-995=5, 995÷5=199, 199+1=200 terms\r\n" );
document.write( "Average term × Number of terms = 502.2×200 = 100500\r\n" );
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document.write( "Edwin

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