document.write( "Question 992067: What would be the next three numbers in this sequence 2,7,9,11 \n" ); document.write( "
Algebra.Com's Answer #611710 by Edwin McCravy(20056) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "Let the first 4 terms be A,B,C, and D\r\n" );
document.write( "\r\n" );
document.write( "A=2, B=7, C=9, D=11\r\n" );
document.write( "\r\n" );
document.write( "We observe that\r\n" );
document.write( "\r\n" );
document.write( "2+7=9, \r\n" );
document.write( "9+2=11\r\n" );
document.write( "\r\n" );
document.write( "And the formula for that is \r\n" );
document.write( "\r\n" );
document.write( "A+B=C, \r\n" );
document.write( "C+A=D\r\n" );
document.write( "\r\n" );
document.write( "Now A and B become what were previously \r\n" );
document.write( "C and D respectively. So A is now 9 and \r\n" );
document.write( "B is now 11.\r\n" );
document.write( "\r\n" );
document.write( "We use the same formula:\r\n" );
document.write( "\r\n" );
document.write( "A+B=C=9+11=20\r\n" );
document.write( "C+A=D=20+9=29\r\n" );
document.write( "\r\n" );
document.write( "So the next two terms are 20 and 29.\r\n" );
document.write( "\r\n" );
document.write( "So now the sequence is 2,7,9,11,20,29\r\n" );
document.write( "\r\n" );
document.write( "---\r\n" );
document.write( "\r\n" );
document.write( "Now A and B become what were previously \r\n" );
document.write( "C and D respectively. So A is now 20 and \r\n" );
document.write( "B is now 29.\r\n" );
document.write( "\r\n" );
document.write( "We use the same formula:\r\n" );
document.write( "\r\n" );
document.write( "A+B=C=20+29=49\r\n" );
document.write( "C+A=D=49+20=69\r\n" );
document.write( "\r\n" );
document.write( "So the next two terms are 49 and 69.\r\n" );
document.write( "\r\n" );
document.write( "So now the sequence is 2,7,9,11,20,29,49,69\r\n" );
document.write( "\r\n" );
document.write( "---\r\n" );
document.write( "\r\n" );
document.write( "Now A and B become what were previously \r\n" );
document.write( "C and D respectively. So A is now 49 and \r\n" );
document.write( "B is now 69.\r\n" );
document.write( "\r\n" );
document.write( "We use the same formula:\r\n" );
document.write( "\r\n" );
document.write( "A+B=C=49+69=118\r\n" );
document.write( "C+A=D=118+49=167\r\n" );
document.write( "\r\n" );
document.write( "So the next two terms are 118 and 167.\r\n" );
document.write( "\r\n" );
document.write( "So now the sequence is 2,7,9,11,20,29,49,69,118,167,...\r\n" );
document.write( "\r\n" );
document.write( "Etc.. etc., etc. \r\n" );
document.write( "\r\n" );
document.write( "Note:  There is never just one patteren for a sequence.\r\n" );
document.write( "This pattern may not have been the pattern your teacher\r\n" );
document.write( "had in mind but it IS a possible pattern.\r\n" );
document.write( "\r\n" );
document.write( "Another possibility is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which gives sequence 2,7,9,11,16,27,47,79,126,191,...\r\n" );
document.write( "\r\n" );
document.write( "and as you see, is entirely different after the first four terms.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I wonder why they are teaching these sequences of integers\r\n" );
document.write( "as if there were only one way to continue them.  I would\r\n" );
document.write( "appreciate it if you would tell me in the thank-you note \r\n" );
document.write( "form below what course you are studying and if there is any \r\n" );
document.write( "textbook for such a course.\r\n" );
document.write( " \r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );