Sequence generators

Question

1,1,2,3,5,8

Answer 1

This is the start of the famous Fibonacci Sequence.  Each term after the first two is found by adding the two preceding terms.

 

2 = 1+1

3 = 1+2

5 = 2+3

8 = 3+5  etc

 

We can define the sequence recursively as follows:

 

  a₁ = 1     a₂ = 1

 

  a_n = a_n-1 + a_n-2 , for n = 3, 4, 5, ...