Patterns and relationships

The following sequences have the same rule but different starting values:

0, 1, 2, 2, 3, 5, 7, 10, 15, 22, 32,…

1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41,…

a) What are the next three terms in each sequence?

b) Explain the rule.

c) What is the relationship between corresponding terms of the two sequences?

BONUS Prove your answer to c)

I don't know what to do

Re: Patterns and relationships

Take 0,1,2:

0+2=2

so you have 0,1,2,2:

1+2=3

0,1,2,2,3

2+3=5

0,1,2,2,3,5 and so on.... Try to explain this..

You should get:

$\displaystyle x_n=x_{n-1}+x_{n-3}$