# 11.1 Arithmetic series ```Activity 11.1 Arithmetic Series
Overview:
This activity is a worksheet that explores the number of seats in a theater, which can be modeled
by an arithmetic series. The worksheet leads students through the process of finding the formula
of the series by asking a series of directed questions. Students are then asked to identify which
of four given series are arithmetic.
Estimated Time Required:
The activity should take approximately 20 minutes.
Technology: None
Concepts:

Arithmetic series and the associated notation
Discussion:
When you generalize the structure of an arithmetic sequence, use caution in introducing the
standard notation that uses subscripts.
Activity 11.1 Arithmetic Series
1. Suppose a theater has 40 rows of seats; the first row contains 18 seats, and the number of
seats increases by 2 per row. How many seats are in the theater?
To answer this question (without adding up every single term), work through the following
steps:
a.) Write a sequence for the number of seats in consecutive rows, starting with 18 (the first
row)
b.) Now, write out the sum you are trying to find (use … in the middle to save space).
c.) By pairing the first and last term, the second and next-to-last term, and so on, do you
notice a pattern? How many seats are in the theater?
d.) Now, find a formula for determining the number of seats in the nth row.
e.) Can you relate the sum you found in part (c) to your formula in part (d) to find a general
formula for the sum of the first n terms of this type of sequence?
2. Which of the following sequences are arithmetic?
a.) an 
1
n
d.) 0.2, 0.02, 0.002,
b.)
3 1 1
, , ,
4 4 4
c.)
an  3  3n
```