1. Arithmetic Sequences & Partial Sums
Section 8.2
Arithmetic Sequences
&
Partial Sums

2. Arithmetic Sequences & Partial Sums
A sequence in which a set number is added to each
previous term is called an arithmetic sequence.
Definition of Arithmetic Sequences
A sequence is arithmetic if the difference between
consecutive terms are the same. So, the sequence
a1, a2, a3, a4, …, an, …
Is arithmetic if there is a number d such that
a2 – a1= a3 – a2 = a4 – a3 = … = d

3. Arithmetic Sequences & Partial Sums
Examples:
Determine if the following sequences are arithmetic, and if so,
determine the common difference, d.

4. Arithmetic Sequences & Partial Sums
How does one determine a particular term in a given
sequence?
The nth term of an Arithmetic Sequence
The nth term of an arithmetic sequence has the form
an = a1 + (n – 1)d
where d is the common difference between consecutive
terms of the sequence.

5. Arithmetic Sequences & Partial Sums
Examples:
1. Find the 40th term of the sequence where a1 = 4 and d = – 2.
2. Determine the formula for the sequence described in #1.
Note: In developing
a formula, only
substitute for a1 and
d. Then simplify.

6. Arithmetic Sequences & Partial Sums
The Sum of a Finite Arithmetic Sequence
The sum of a finite arithmetic sequence with n terms
is given by

7. Arithmetic Sequences & Partial Sums
Examples:
1. Find the sum of the
first 20 multiples of 4.
2. Find the sum of the 10 terms
defined by an = 3n – 4

8. Arithmetic Sequence & Partial Sum
Example:
An auditorium has 30 rows of seats. There are 15 seats in the
first row and then an additional seat added on each end in each
row thereafter. What is the seating capacity of the auditorium?

9. Arithmetic Sequences & Partial Sums
What you should know:
1. Apply the formula for an arithmetic sequence.
2. Apply the formula for finding the nth partial sum of an
arithmetic sequence.