11.2 Arithmetic Series
 a + an 
The sum of the first n terms of an arithmetic series is: S n = n  1
.
 2 
Sn is the mean of the first and nth terms, multiplied by the number of terms.
Steps for Finding a Sum of an Arithmetic Series
1.) Write a rule for the nth term (i.e. find an).
2.) Calculate the final term, an .
 a + an
3.) Substitute n, a1 , and an into the formula S n = n  1
 2
4.) Simplify.

.

Ex: Consider the arithmetic series 4 + 7 + 10 + 13 + 16 + 19 +…
a) Find the sum of the first 30 terms.
b) Find n such that Sn = 175.
Ex: Consider the arithmetic series 20 + 18 + 16 + 14 + …
a) Find the sum of the first 25 terms.
b) Find n such that Sn = −760.
Ex: Find the sum of the arithmetic series.
12
c)
(2 + 7n )
∑
n
=1
28
d)
( −2 + 4n )
∑
n
=1
Arithmetic Series in Real Life
Seating Capacity: The first row of a concert hall has 25 seats, and each row after
the first has one more sear than the row before it. There are 32 rows of seats.
a) What is the total number of seats in the concert hall?
b) Thirty-five students from the same class want to sit in the same row. How
close to the front can they sit?
Piping: A construction company is laying natural gas pipeline. Several sections of
pipe have been laid in a pile at the construction site. There are 12 sections of pipe
in the bottom row of the pile. Each row has one less pipe than the row below it.
There are 8 rows of pipe.
a) What is the total number of pipe sections in the pile?
b) Suppose 3 more rows of pipe are added to the pile. How many additional
pipe sections will the pile have?