11.1 Arithmetic series

Activity 11.1 Arithmetic Series
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
Arithmetic series and the associated notation
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
a.) Write a sequence for the number of seats in consecutive rows, starting with 18 (the first
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 
d.) 0.2, 0.02, 0.002,
3 1 1
, , ,
4 4 4
an  3  3n