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__The nth term of an Arithmetic Sequence__

The nth term of an arithmetic sequence can be found using this formula, shown in Figure 1.

In this formula,

*a*is the first term,

*n*is the term number and

*d*is the common difference.

Consider this sequence

2, 5, 8, 11,...

Here the first term is 2 and the common difference is 5-2, or 3.

or, simplified, 3n-1.

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__The Sum of an Arithmetic Sequence__

The sum of and arithmetic sequence can be found using this formula.

In this case, n is the number of numbers being summed.

Consider the previous sequence.

If we had to sum the first ten numbers in this sequence, we would put the values of n, a and d into the formula.

or 155.

Try these questions.

Pictures from: http://www.a-levelmathstutor.com/arithmetic.php

http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-apgp-2009-1.pdf

Congratulations.

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