document.write( "Question 1204618: The pattern forming the irrational number 0.12340432100123400043210000... continues indefinitely. What is the 1945th digit in this pattern?
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Algebra.Com's Answer #840982 by mccravyedwin(407) $\"\"$ $\"About$

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document.write( "[The first time I did this problem I forgot to count the 0 digit before the\r\n" );
document.write( "decimal point as the 1st digit. Here is the correction. I'll delete the first\r\n" );
document.write( "one.]\r\n" );
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document.write( "The 1's at the beginning of a 1234 appear at digits 2, 13, 28, 47. \r\n" );
document.write( "Then I found the quadratic function that passes through (1,2), (2,13), (3,28),\r\n" );
document.write( "by substituting those points in , and finding a=2, b=5, and\r\n" );
document.write( "c=-5. So the equation is:\r\n" );
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document.write( ", where the yth term is a 1 at the beginning of a 1234.\r\n" );
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document.write( "So I set y=1945 and solved the equation:\r\n" );
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document.write( " and got x as 30 exactly.\r\n" );
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document.write( "Then I substituted the whole part x=30 in\r\n" );
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document.write( "So the 1945th digit is a 1 at the beginning of a 1234.\r\n" );
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document.write( "Edwin

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