We know the Fibonacci sequence is generated by the recursion rule fn = fn-1 + fn-2 where f1 = 1 and f2 = 1.
a. Add up the first 10 Fibonacci numbers; then multiply the 7th Fibonacci number by 11. What do you notice?
b. Create another sequence of numbers using the recursion rule fn = fn-1 + fn-2. Pick your own values for f1 and f2. Repeat part (a) using the numbers from your new sequence.
c. Create a sequence using the recursion rule fn = fn-1 + fn-2, but let f1 = a and f2 = b. List the first 10 terms in the sequence. What do you notice about the terms in the sequence? Repeat part (a) with the terms you generated and describe this property of the Fibonacci sequence. Is it true that the sum of any 10 consecutive Fibonacci numbers is a multiple of 11?
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