Arithmetic Series (Jump to: Lecture | Video )

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.