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Continue the pattern and write a pattern rule.

1,1,2,4,7,11,..,..

I'm really confused about this pattern.

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

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  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.

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