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# Math

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in November 2020. This work is licensed under a Creative Commons BY 4.0 International License ## Arithmetic Sequences

##### An arithmetic series is a series in which the difference between a term and next term is a constant. This constant is called the common difference. The general form of an arithmetic sequence is given by: ##### in the above equation, is the first term of the sequence and is the common difference. Note that each term of the sequence differs from the pervious term by . The last term of the sequence, denoted by is given by: ##### Example: Is the following sequence an arithmetic sequence? ##### If a sequence is an arithmetic sequence, the difference between successive terms has to be a constant. We have to find the difference between the first term and the second term, the second term and the term term etc. If the difference is a constant, then the sequence is an arithmetic sequence. ##### Example: For an arithmetic sequence, . Find .

For an arithmetic sequence, the general term is , therefore for we get: ##### We use the formula for the general term of an arithmetic sequence and substitute the given values in the formula: ##### therefore, we get: 