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# 3.1 - Linear & Quadratic nth Terms

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Author: Kyle Webb
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Use linear equations and quadratic equations to find a formula that will allow you to find any term in a sequence (or the nth term).

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Tutorial

## Linear nth Terms

If you have a sequence with a constant first common difference, it can be defined using a linear equation.  The following formula can be used to find any nth term in the sequence. Where:

a is the first term in the sequence

d is the common difference between the terms

## Quadratic nth Terms

When you cannot find a constant first common difference, look at the second differences.  If that second difference is constant, you can define the sequence using a quadratic equation.  The following formula can be used to find any term in the sequence. Where:

a is the first term in the sequence

d is the difference between the first and the second term

c is the common second difference you found.

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