document.write( "Question 1146196: Find the sum of:\r
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Algebra.Com's Answer #767484 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Find the sum of:
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That is the sequence 1, 3, 5, 7, 9, …\r\n" );
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document.write( "a1 = first term = 1\r\n" );
document.write( "d = common difference = 2nd-1st = 3-1 = 2\r\n" );
document.write( "formula for sum of first n terms:  Sn = [n/2][2a1+(n-1)d]  \r\n" );
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document.write( "Sn = [n/2][2a1+(n-1)d]  \r\n" );
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document.write( "Sn = [n/2][2∙1+(n-1)2]\r\n" );
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document.write( "Sn = [n/2][2+2(n-1)]\r\n" );
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document.write( "Sn = [n/2][2+2n-2]\r\n" );
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document.write( "Sn = [n/2][2n] \r\n" );
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document.write( "Sn = [n][n]\r\n" );
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document.write( "Sn = n²

\n" ); document.write( "b) the first 'n' even positive integers
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document.write( "That is the sequence 2, 4, 6, 8, 10, …\r\n" );
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document.write( "a1 = first term = 2\r\n" );
document.write( "d = common difference = 2nd-1st = 4-2 = 2\r\n" );
document.write( "formula for sum of first n terms:  Sn = [n/2][2a1+(n-1)d]  \r\n" );
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document.write( "Sn = [n/2][2a1+(n-1)d]  \r\n" );
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document.write( "Sn = [n/2][2∙2+(n-1)2]\r\n" );
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document.write( "Sn = [n/2][4+2(n-1)]\r\n" );
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document.write( "Sn = [n/2][4+2n-2]\r\n" );
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document.write( "Sn = [n/2][2n+2]\r\n" );
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document.write( "Sn = [n/2][2(n+1)] \r\n" );
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document.write( "Sn = n(n+1)\r\n" );
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c) the first 'n' positive integers and find 'n' if the sum is 210.
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document.write( "That is the sequence 1, 2, 3, 4, 5, …\r\n" );
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document.write( "a1 = first term = 1\r\n" );
document.write( "d = common difference = 2nd-1st = 2-1 = 1\r\n" );
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document.write( "          Sn = [n/2][2a1+(n-1)d], \r\n" );
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document.write( "         210 =  [n/2][2(1)+(n-1)(1)]\r\n" );
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document.write( "         210 =  [n/2][2+n-1]\r\n" );
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document.write( "         210 =  [n/2][n+1]\r\n" );
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document.write( "Multiply both sides by 2 to clear the fraction:\r\n" );
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document.write( "         420 = n[n+1]\r\n" );
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document.write( "         420 = n² + n\r\n" );
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document.write( "           0 = n² + n - 420\r\n" );
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document.write( "n² + n - 420 = 0\r\n" );
document.write( "(n+21)(n-20) = 0\r\n" );
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document.write( "n+21=0;   n-20=0\r\n" );
document.write( "   n=-21;    n=20\r\n" );
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document.write( "Discard the negative value since the number of terms is always \r\n" );
document.write( "a positive whole number.\r\n" );
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document.write( "Answer:  20\r\n" );
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document.write( "Edwin

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