Getting fun in Fibonnaci Sequence
Probability
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pending
1,1,2,3,5,8,13... is the Fibonacci sequence. The third number is the sum of first and second number(2=1+1). The forth number is the sum of second and third number(3=2+1) and the list goes on. Find the remainder of the 2009th number in this sequence when it is divided by 8.
The answer is 5.
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1 solution
If we write the remainder when the numbers in the sequence are divided by 8, the remainders are 1,1,2,3,5,0,5,5,2,7,1,0,1,1,2,3,5,0,5,5,2,7,1,0... as we can see, the sequence is also in the fibonnaci sequence and the cycle is repeated in every 12 numbers (1,1,2,3,5,0,5,5,2,7,1,0). Hence, the remainder of 2009th number in the fibonacci sequence can be found by divided it by 12. The remainder is 5, which means that the remainder is at the 5th position in the 12 numbers, which is 5!