document.write( "Question 822545: what is the 20th term of 16,49,104,181 ? \n" ); document.write( "
Algebra.Com's Answer #495044 by Edwin McCravy(20065)\"\" \"About 
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document.write( "16,49,104,181\r\n" );
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document.write( "I always first check the sequence of differences to see\r\n" );
document.write( "if I can recognize a pattern:\r\n" );
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document.write( "2nd term - 1st term =   49-16 = 33 = 11×3\r\n" );
document.write( "3rd term - 2nd term =  104-49 = 55 = 11×5 \r\n" );
document.write( "4th term - 3rd term = 181-104 = 77 = 11×7\r\n" );
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document.write( "So we can now see the pattern.\r\n" );
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document.write( " 1.    Start with 16, then\r\n" );
document.write( " 2.    16 + 11×3  =   49\r\n" );
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document.write( "and the multiple of 11, which is 3, is 1 less than twice the term\r\n" );
document.write( "number, which is 2. \r\n" );
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document.write( " 3.    49 + 11×5  =  104 =\r\n" );
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document.write( "16 + 11×3 + 11×5\r\n" );
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document.write( "and the multiple of 11, which is 5, is 1 less than twice the term\r\n" );
document.write( "number, which is 3.\r\n" );
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document.write( " 4.   104 + 11×7  =  181 =\r\n" );
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document.write( "16 + 11×3 + 11×5 + 11×7\r\n" );
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document.write( "and the multiple of 11, which is 7, is 1 less than twice the term\r\n" );
document.write( "number, which is 4\r\n" );
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document.write( "Therefore to find the 20th term, we start with 16 and add\r\n" );
document.write( "19 terms.  So the 20th term is\r\n" );
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document.write( "16+\"sum%2811%282k-1%29%2Ck=2%2C20%29\" =\r\n" );
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document.write( "Factor out 11 from the sun:\r\n" );
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document.write( "16+\"11%2Asum%28%282k-1%29%2Ck=2%2C20%29\" =\r\n" );
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document.write( "Break up the sum into two sums:\r\n" );
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document.write( "16+\"11%2A%28sum%28%282k%29%2Ck=2%2C20%29-sum%28%281%29%2Ck=2%2C20%29%29++\" =\r\n" );
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document.write( "Factor out 2 from the first sum:\r\n" );
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document.write( "16+\"11%2A%282%2Asum%28%28k%29%2Ck=2%2C20%29-sum%28%281%29%2Ck=2%2C20%29%29++\" =\r\n" );
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document.write( "The sum \"sum%28%28k%29%2Ck=2%2C20%29\" is the sum of an arithmetic sequence\r\n" );
document.write( "with a1 = 2 and a19 = 20, and d=1\r\n" );
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document.write( "Sn = \"n%2F2\"(a1 + an)\r\n" );
document.write( "S19 = \"19%2F2\"(2 + 20) = \"19%2F2\"(22) = 209\r\n" );
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document.write( "And \"sum%28%281%29%2Ck=2%2C20%29%29\" is the sum of 19 ones, which is 19.\r\n" );
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document.write( "Substituting in:\r\n" );
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document.write( "16+\"11%2A%282%2Asum%28%28k%29%2Ck=2%2C20%29-sum%28%281%29%2Ck=2%2C20%29%29++\" =\r\n" );
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document.write( "We have\r\n" );
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document.write( "16+11·(2·209-19) =\r\n" );
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document.write( "4405.\r\n" );
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document.write( "Edwin
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