document.write( "Question 1208787: The pattern forming the irrational number 0.3450543003450005430000... continues indefinitely. What is the 81403rd digit in this pattern?
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Algebra.Com's Answer #847274 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "0.3450543003450005430000\r\n" );
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document.write( "Here is the problem assuming the introductory 0 on the left of the decimal is the 1st digit\r\n" );
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document.write( "The 4's occur in positions 3, 7, 12, 18, ...\r\n" );
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document.write( "Its sequence of first differences 4, 5, 6,... is linear, so the\r\n" );
document.write( "sequence of positions of 4s is quadratic.\r\n" );
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document.write( "Let the general term of 3, 7, 12, 18, ... be \r\n" );
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document.write( "Solve that and get A=0.5, B=2.5, C=0\r\n" );
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document.write( "So the general term for the positions of 4's is \r\n" );
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document.write( "So let's find the position of the 4 nearest (or 'at') the 81403rd term by \r\n" );
document.write( "setting\r\n" );
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document.write( "Solving that with a quadratic program on my TI-84 graphing calculator:\r\n" );
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document.write( "n=401 and n=-406 \r\n" );
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document.write( "That has solution 401 (Ignore the negative), so the 81403rd digit is a 4.\r\n" );
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document.write( "Answer = 4\r\n" );
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document.write( "It's easier when we consider the 0 to the left of the decimal as the\r\n" );
document.write( "first digit.\r\n" );
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document.write( "In the olden days, people didn't, as a rule, put a 0 before the decimal\r\n" );
document.write( "in decimal fractions between -1 and 1, as they do today.  We would just write,\r\n" );
document.write( "say, .5, not 0.5, and -.75, not -0.75 and:\r\n" );
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document.write( ".3450543003450005430000... not 0.3450543003450005430000...\r\n" );
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document.write( "I'm an old fogy, so that's why I didn't consider the initial 0 before\r\n" );
document.write( "the decimal as the first digit in my other answer. LOL\r\n" );
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document.write( "Edwin

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