Question 200754
Looking at the sequence 1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9



we can color code all the odd entries in red and the even entries in green like so:



<font color="red">1</font><font color="green">, 1, </font><font color="red">1</font><font color="green">, 2, </font><font color="red">2</font><font color="green">, 3, </font><font color="red">3</font><font color="green">, 4, </font><font color="red">5</font><font color="green">, 5, </font><font color="red">8</font><font color="green">, 6, </font><font color="red">13</font><font color="green">, 7, </font><font color="red">21</font><font color="green">, 8, </font><font color="red">34</font><font color="green">, 9, </font>




Looking above, we see that the 1st, 3rd, 5th, 7th, etc. terms are:


1,1,2,3,5,8,13,21,34,...


which follow the Fibonacci sequence



and the 2nd, 4th, 6th, 8th, etc. terms are



1,2,3,4,5,6,7,8,9,...



So the next term will be the next Fibonacci number which is: 21+34=55


and the next number after that is the next integer after 9, which is 10.


So the sequence then becomes



1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9,<font color=red>55</font>,<font color=red>10</font>,...



and this pattern continues indefinitely. So you can use the same logic applied above to find the next set of numbers in the sequence.