eli5: Characteristics of partial sums in the Fibonacci Sequence

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Are any set of 10 consecutive terms always divisible by 11 or does 11 increase as the numbers increase?

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Anonymous 0 Comments

It’s always 11.

The sum of 10 consecutive numbers in a Fibonacci Sequence where the first number of the sequence is a and the second number in the sequence is b is 55a + 88b = 11(5a + 8b).

It actually doesn’t matter what the first two numbers are! As long as you follow the Fibonacci Rule where the next number is equal to the sum of the previous two, you get a number that is divisible by 11.

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