document.write( "Question 694948: What are the next three terms in each sequence?\r
\n" ); document.write( "\n" ); document.write( "9,109,209,309,409\r
\n" ); document.write( "\n" ); document.write( "1/2, 1/2,3/8, 1/4, 5/32 \n" ); document.write( "

Algebra.Com's Answer #428263 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "9, 109, 209, 309, 409\r\n" );
document.write( "\r\n" );
document.write( "Consider the first term 9, to be written 009, then we have:\r\n" );
document.write( "\r\n" );
document.write( "009, 109, 209, 309, 409\r\n" );
document.write( "\r\n" );
document.write( "Then the last two digits of them all are 09 and the\r\n" );
document.write( "first digits go 0,1,2,3,4.  So the next three are, \r\n" );
document.write( "of course 5,6,7.  Putting 09 after them we get:\r\n" );
document.write( "\r\n" );
document.write( "009, 109, 209, 309, 409, 509, 607, 709.\r\n" );
document.write( "\r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( ", , , , \r\n" );
document.write( "\r\n" );
document.write( "We notice that all the denominators are powers of 2.\r\n" );
document.write( "\r\n" );
document.write( "We notice that the 1st term has a numerator of 1 and a denominator of .\r\n" );
document.write( "We notice that the 3rd term has a numerator of 3 and a denominator of .\r\n" );
document.write( "We notice that the 5th term has a numerator of 5 and a denominator of .\r\n" );
document.write( "\r\n" );
document.write( "So the 1st, 3rd, and 5th terms are , , and  \r\n" );
document.write( "\r\n" );
document.write( "That's a pattern with the 3 odd-numbered terms, so for the odd-numbered\r\n" );
document.write( "terms, we have the pattern  where n is odd 1, 3, and 5.\r\n" );
document.write( "\r\n" );
document.write( "So we wonder if the two even numbered terms might follow\r\n" );
document.write( "the same pattern. \r\n" );
document.write( "\r\n" );
document.write( "They would if the 2nd term, , were , \r\n" );
document.write( "and the 4th term, , were .  Sure enough\r\n" );
document.write( "they are, since  =  = , and\r\n" );
document.write( " =  = \r\n" );
document.write( "\r\n" );
document.write( "So we have the pattern.  The nth term is \r\n" );
document.write( "\r\n" );
document.write( "So the 6th term is  =  = ,\r\n" );
document.write( "the 7th term is  = , and\r\n" );
document.write( "the 8th term is  =  = \r\n" );
document.write( "\r\n" );
document.write( ", , , , , , , .\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );