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,_
Answer by jim_thompson5910(35256)   (Show Source):
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
we can color code all the odd entries in red and the even entries in green like so:
1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 8, 6, 13, 7, 21, 8, 34, 9,
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
1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9,55,10,...
and this pattern continues indefinitely. So you can use the same logic applied above to find the next set of numbers in the sequence.
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