document.write( "Question 848987: Calculate the sum of all natural numbers from 100 to 200 both inclusive which are not divisible by 6 \n" ); document.write( "
Algebra.Com's Answer #511685 by AnlytcPhil(1806)\"\" \"About 
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Calculate the sum of all natural numbers from 100 to 200 both inclusive which are not divisible by 6
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document.write( "First we'll find the sum of all natural numbers from 100 to 200, inclusive.\r\n" );
document.write( "Then we'll find the sum of all the multiples of 6 from 102 to 198, inclusive.\r\n" );
document.write( "Then we'll subtract them.\r\n" );
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document.write( "All natural numbers from 100 to 200, inclusive.\r\n" );
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document.write( "That's the arithmetic sequence 100,101,102,103,...,200\r\n" );
document.write( "with a1=100, d=1, and an=200\r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "To find the number of terms:\r\n" );
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document.write( "200 = 100 + (n-1)1\r\n" );
document.write( "100 = n-1\r\n" );
document.write( "101 = n\r\n" );
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document.write( "We use the sum formula\r\n" );
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document.write( "Sn = \"n%2F2\"(a1 + an) \r\n" );
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document.write( "S101 = \"101%2F2\"(100 + 200) = \"expr%28101%2F2%29%28300%29\" = 15150\r\n" );
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document.write( "The multiples of 6 from 102 to 198, inclusive, is the arithmetic\r\n" );
document.write( "sequence 102,108,114,...,198, with a1=100, d=1, and an=200\r\n" );
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document.write( "To find the number of terms:\r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "198 = 102 + (n-1)6\r\n" );
document.write( "198 = 102+6n-6 \r\n" );
document.write( "198 = 96+6n\r\n" );
document.write( "102 = 6n\r\n" );
document.write( " 17 = n\r\n" );
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document.write( "We use the sum formula\r\n" );
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document.write( "Sn = \"n%2F2\"(a1 + an) \r\n" );
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document.write( "S7 = \"17%2F2\"(102 + 198) = \"expr%2817%2F2%29%28300%29\" = 2550\r\n" );
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document.write( "Subtracting,  15150-2550 = 12600.\r\n" );
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document.write( "Answer = 12600.\r\n" );
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document.write( "Edwin
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