Arithmetic Sequences

Arithmetic sequences are sequences where a number is added or subtracted from the previous number to get the next number.

The nth term of an Arithmetic Sequence

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

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.

The nth term for this sequence would be:

or, simplified, 3n-1.

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.




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