document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704501>Question 704501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the next two numbers in this sequence, 4,9,7,14,10,19,13,24,16,29  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434114 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at the odd numbered terms (in red)\r<BR>\n" );
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document.write( "<font color=\"red\">4</font>,9,<font color=\"red\">7</font>,14,<font color=\"red\">10</font>,19,<font color=\"red\">13</font>,24,<font color=\"red\">16</font>,29\r<BR>\n" );
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document.write( "Going from 4, to 7, to 10, etc tells us we're adding 3 to each term. This is because 4+3 = 7, 7+3 = 10, etc.\r<BR>\n" );
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document.write( "So part of the rule is this: if n is an odd number, then you use the rule: an = 3n+1 where n starts at n = 1. This rule only works if n is odd though.\r<BR>\n" );
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document.write( "If n is even, then we have this sequence (look at the above sequence, but instead of the red terms, focus on the black terms): 9, 14, 19, 24, 29\r<BR>\n" );
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document.write( "Now we're adding 5 to each term. So the rule is: if n is even, then use the formula an = 5n+4\r<BR>\n" );
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document.write( "So in the end, we have this rule\r<BR>\n" );
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document.write( "If n is odd, use the formula an = 3n+1, where n starts at n = 1<BR>\n" );
document.write( "If n is even, use the formula an = 5n+4, where n starts at n = 2\r<BR>\n" );
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document.write( "That completes the entire sequence because any number is either even or odd.\r<BR>\n" );
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document.write( "The next term would be odd, so use the odd formula: 3n+1 = 3(6)+1 = 19. So the next term after 29 is 19\r<BR>\n" );
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document.write( "The term after that is even, so use 5n+4 = 5(6)+4 = 34.\r<BR>\n" );
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document.write( "So the next two terms are: 19 and 34\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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