What is the answer and how did you work it out?

Question

Carol has a rule for a sequence of numbers
Her rule is
                 The next number is the sum of the two previous numbers.
Use Carlo's rule to write in the three missing numbers
Something, something, something, 0, 1,1,2,3,5,8

Answer

The sequence is:

2 -1 1    0 1 1 2 3 5 8

Because you know that x(n) = x(n-1) + x(n-2), you also know x(n-2) = x(n) - x(n-1). So you can work backwards as well as forwards.

What is the answer and how did you work it out?

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