Part 1) When you add together three consecutive Fibonacci numbers (like this 1+1+2=4
1+2+3=6
2+3+5=10
3+5+8=16) if you take the middle number and multiply it by two it gives you the answer to the previous question. Also the third number when doubled equals the answer to that same question.
Part 2) If you choose any four consecutive Fibonacci numbers and add the first and last number the sequence looks like this:
1+3=4 divided by 2 = 2
1+5=6 divided by 2 = 3
2+8=10 divided by 2 = 5
...
From this sequence we have noticed that the answers of the equations in order ascends in the Fibonacci sequence. Also the answer is the third term in the sequence of for numbers. Another thing we have noticed is that when you add the first and last numbers of the sequence together the answer is the same to when you add three consecutive numbers together in order - the first question.
Part 3) If you add six consecutive Fibonacci numbers then divide by four the sequence looks like this:
1+1+2+3+5+8=20 divided by 4 = 5
1+2+3+5+8+13=32 divided by 4 = 8
2+3+5+8+13+21=52 divided by 4 = 13
3+5+8+13+21+34=84 divided by 4 = 21
...
The answers (just like in the second question) go up in the Fibonacci sequence and the second last number in the six consecutive numbers is the overall answer to the question.
Solution
152979
Problem / game
First name
Amy Rickwood, Emily Smith, Rachael Lever, Hollie-R
School
Oundle and Kings Cliffe Middle School
Country
Age
13