document.write( "Question 934667: what is the sum of 2+3+5+6+8+9+....2n terms? \n" ); document.write( "
Algebra.Com's Answer #567741 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I think the \"2n terms\" should have been \"3n terms\", because with \r\n" );
document.write( "2n terms, there will have to be three formulas, depending on whether \r\n" );
document.write( "2n is a multiple of 3, 1 less than a multiple of 3, or 1 more than \r\n" );
document.write( "a multiple of 3.\r\n" );
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document.write( "So I'm going to do the problem assuming that the 2n should have been 3n,\r\n" );
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document.write( "OK?  Let me know.\r\n" );
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document.write( "It's the sum of two arithmetic sequences:\r\n" );
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document.write( "S1 = 2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+...+3n+1 (to 3n terms) \r\n" );
document.write( "S2 =    -4    -7    -10      -13      -16+...      (to n terms   \r\n" );
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document.write( "There are 3n terms of the first sequence and n terms of the second sequence.\r\n" );
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document.write( "We use the formula:\r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\"\r\n" );
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document.write( "We substitute \"3n\" for \"n\", \"a%5B1%5D=2\", \"a%5B3n%5D=3n%2B1\"\r\n" );
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document.write( "\"S1%5B3n%5D=expr%283n%2F2%29%282%2B3n%2B1%29\"\r\n" );
document.write( "\"S1%5B3n%5D=expr%283n%2F2%29%283n%2B3%29\"\r\n" );
document.write( "\"S1%5B3n%5D=expr%283n%2F2%29%283%28n%2B1%29%29\"\r\n" );
document.write( "\"S1%5B3n%5D=expr%289n%2F2%29%28n%2B1%29\" \r\n" );
document.write( "\"S1%5B3n%5D=9n%28n%2B1%29%2F2\" = the sum of the 1st sequence.\r\n" );
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document.write( "We use the formula \r\n" );
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document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29\"\r\n" );
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document.write( "to find the sum of the 2nd sequence\r\n" );
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document.write( "\"a%5B1%5D=-4\", \"d=-3\" \r\n" );
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document.write( "\"S2%5Bn%5D=expr%28n%2F2%29%282%28-4%29%2B%28n-1%29%28-3%29%29\"\r\n" );
document.write( "\"S2%5Bn%5D=expr%28n%2F2%29%28-8-3n%2B3%29%29\"\r\n" );
document.write( "\"S2%5Bn%5D=expr%28n%2F2%29%28-5-3n%29%29\"\r\n" );
document.write( "\"S2%5Bn%5D=n%28-5-3n%29%29%2F2\"\r\n" );
document.write( "\"S2%5Bn%5D=-n%285%2B3n%29%29%2F2\"\r\n" );
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document.write( "So the required sum is\r\n" );
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document.write( "\"S1%5B3n%5D-S1%5Bn%5D\"\"%22%22=%22%22\"\"9n%28n%2B1%29%2F2-%28n%285%2B3n%29%29%2F2\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"%289n%28n%2B1%29-n%285%2B3n%29%29%2F2\"\"%22%22=%22%22\"\"%289n%5E2%2B9n-5n-3n%5E2%29%2F2\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"6n%5E2%2B4n%29%2F2\"\"%22%22=%22%22\"\"3n%5E2%2B2n\"\"%22%22=%22%22\"\"n%283n%2B2%29\"\r\n" );
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document.write( "Sum of the first 3n terms = \"n%283n%2B2%29\"\r\n" );
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document.write( "Edwin
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