Is this Fibonacci number even or odd?
Level
pending
If n = the combination of all numbers from 1 to 1000 (12345678910111213141516...), what is F_{n} ? Try solving it without a calculator.
Neither
Odd
Not enough information
Even
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1 solution
First of all, I'm sorry about that failed LaTeX attempt, I looked it up on the style guide, but it still came out weird... anyways, Even + Even = Even Even + Odd = Odd Odd + Even = Odd Odd + Odd = Even In the Fibonacci sequence, the first two terms are odd. That means the third (F 3) is 2. F 4 = F 3 + F 2, or Even + Odd = Odd, so F 4 = Odd. F 5 = F 4 + F 3, or Odd + Even = Odd, so F 5 is odd. F 6 = F 5 + F 4, and since both F 5 and F 4 are odd, F 6 = Odd + Odd = Even. This pattern repeats. So, when n is divisible by 3, F n will be even. So, the sum of all of the digits in the numbers 1 to 1000 = (1000(1001))/2 = 500,500.This number is not divisible by three, so F (123456789101112...) is not even, it is odd. I still can't get the hang of LaTeX. F 2 = F sub 2.