Arithmetic Series (Jump to: Lecture | Video )


A series is the sum of the terms of a sequence.

Below we have a representation of theatre seating. The 1st row has just 3 seats, while the 8th row has 10 seats.

Figure 1.

How many people can sit in the first five rows? To find the answer, we simply add the first five rows:

3 + 4 + 5 + 6 + 7 = 25 people

This is an arithmetic series.

Figure 2.
Sum of an Arithmetic Series

The sum for the first n terms of an arithmetic series is given by the equation:

where n is the number of terms, and a is each individual term.

So, for our example the total sum for the first 7 rows is equal to:

Figure 3.

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