Question

Continue the pattern and write a pattern rule.
1,1,2,4,7,11,..,..

I'm really confused about this pattern.

Answer 1

I can give you a hint. The numbers are increasing in an addition pattern. They are added by a number.

Answer 2

The differences between consecutive pairs:
0,1,2,3,4,...
which means the second differences are:
1,1,1,1,...
Thus it can be expressed as a quadratic function
I got this by:

let the function be y = ax^2 + bx + c
and subbed in the points (1,1), (2,1), (3,2), that's all I needed
This gave me three equations in the variables a, b, and c
I assume you know how to solve such a system.
Let me know what you get.