Question

Finish the sequence 1,1,2,3,5,8,_,_,_

Answer 1

The Fibonacci sequence has to be thought of in these terms:

F₀, F₁, F₂, F₃, F₄, F₅, F₆, F₇, etc, etc

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Now:

F₀=0

F₁=1

The formula you use to get the other numbers is:

$F_{n} = F_{n-1} + F_{n-2}$

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So:

$F_{2} = F_{2-1} + F_{2-2} = F_{1} + F_{0} =1+0=1$

And:

$F_{3}= F_{3-1} + F_{3-2} = F_{2} + F_{1} =1+1=2$

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If you continue using the formula, you should get a sequence that starts off like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc, etc

Answer 2

This is a Fibonacci sequence
1; 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
next terms:
5 + 8= 13
8 +13 = 21
13 + 21 = 34