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3.1 - Linear & Quadratic nth Terms

3.1 - Linear & Quadratic nth Terms

Author: Kyle Webb
Description:

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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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.

f left parenthesis n right parenthesis equals d n plus left parenthesis a minus d right parenthesis

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.

f left parenthesis n right parenthesis equals a plus d left parenthesis n minus 1 right parenthesis plus fraction numerator c left parenthesis n minus 1 right parenthesis left parenthesis n minus 2 right parenthesis over denominator 2 end fraction

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.