Can you use some of the methods above to explain why they happen?ġ. Zach found some other Fibonacci Surprises. Spiros and George, from Hazelwood School, and Yash, from Tanglin Trust School, Singapore explained why we end up with a Fibonacci sequence:įrom here on, $F_n$ will be used to denote the $n^$, i.e. This gives the usual Fibonacci sequence, but without the first four terms. This gives the usual Fibonacci sequence, but without the first two terms.ģ. The first sequence of numbers is formed as a Fibonacci sequence, but starts from $4$ and $6$ instead of $1$ and $1$.Ģ. Mikaeel, from Marlborough Primary School, Lera and Ahmed, from Harbinger School, and Ashley, from Brookfield Community School, noticed that the numbers are in aġ. This time the pattern is a Fibonacci sequence starting from $5$ and $8$, so the pattern is: ODD, EVEN, ODD, ODD, EVEN, ODD. Īlso, all the numbers are integers, since, from our initial observation, if we choose four consecutive Fibonacci numbers, then the first and the last will either be both odd or both even, so their sum will be even.ģ. The second sequence is a Fibonacci sequence starting from $2$ and $3$, so the pattern of odd and even numbers is: EVEN, ODD, ODD, EVEN, ODD, ODD. Therefore, their sum will be an even number.Ģ. This makes sense since, from any three consecutive Fibonacci numbers, one is even and the other two are odd (which follows from our initial observation). For the first sequence, we noticed that all the resulting numbers are even. This made sense, since it starts with two odd numbers ($1, 1$) and the sum ODD + ODD = EVEN and EVEN + ODD = ODD.ġ. The Fibonacci sequence is: ODD, ODD, EVEN, ODD, ODD, EVEN. We noticed that the numbers in the Fibonacci sequence appear in a pattern regarding odd and even numbers. Brian and Hugh, from DCB, South Korea, and Irie-Rose, from St Phillip's Primary School, made some observations about the pattern of odd and even numbers:
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