Arithmetic Series
Key points
- An arithmetic series is the sum of the terms in an arithmetic sequence.
- There are two types of series – finite and infinite.
- There are two main formulae to solve for the sum of a finite arithmetic series.
- The sum of an infinite arithmetic series is either positive or negative infinity.
Arithmetic Series is the sum of the terms in an arithmetic sequence. A general model of an arithmetic series is seen to the right.
- A finite arithmetic series is the sum of the terms of an arithmetic sequence to a given number of terms.
- An infinite arithmetic series is the sum of all of the terms in an infinite arithmetic sequence.
Formula Booklet
There are two formula booklet equations for the sum of a finite arithmetic series, shown to the left.
- Use the first one if you don’t know the value of the last term.
- Use the second one if you don’t know the common difference between each term.
Infinite arithmetic series have a sum of either positive or negative infinity, depending on the value of the common difference.
- If the common difference is positive, or you are adding between terms, the sum of the series is positive infinity.
- This is because you are adding positive numbers infinitely.
- If the common difference is negative, or you are subtracting between terms, the sum of the series is negative infinity.
- This is because you are adding negative numbers infinitely.
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