document.write( "Question 200754: state the next number in the sequence 1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9,_ \n" ); document.write( "
Algebra.Com's Answer #151007 by jim_thompson5910(35256)![]() ![]() ![]() You can put this solution on YOUR website! Looking at the sequence 1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "we can color code all the odd entries in red and the even entries in green like so:\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 8, 6, 13, 7, 21, 8, 34, 9, \r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Looking above, we see that the 1st, 3rd, 5th, 7th, etc. terms are:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "1,1,2,3,5,8,13,21,34,...\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "which follow the Fibonacci sequence\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "and the 2nd, 4th, 6th, 8th, etc. terms are\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,7,8,9,...\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the next term will be the next Fibonacci number which is: 21+34=55\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "and the next number after that is the next integer after 9, which is 10.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the sequence then becomes\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9,55,10,...\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "and this pattern continues indefinitely. So you can use the same logic applied above to find the next set of numbers in the sequence. \n" ); document.write( " |