1. ©2001 by R. Villar All Rights Reserved
Sequences and Series
©2001 by R. Villar
All Rights Reserved

2. Arithmetic Sequences and Series
Arithmetic Sequence: sequence whose consecutive terms have a common difference.
Example: 3, 5, 7, 9, 11, 13, ...
The terms have a common difference of 2.
The common difference is the number d.
Example: Is the sequence arithmetic? –45, –30, –15, 0, 15, 30
Yes, the common difference is 15
How do you find any term in this sequence?
To find any term in an arithmetic sequence, use the formula Un = U1 + (n – 1)d where d is the common difference.

3. Un = U1 + (n – 1)d U1 = 3 d = 5 Un = 3 + (n – 1)5
Example: Find a formula for the nth term of the arithmetic sequence in which the common difference is 5 and the first term is 3.
Un = U1 + (n – 1)d
U1 = 3 d = 5
Un = 3 + (n – 1)5

4. Example: If the common difference is 4 and the fifth term is 15, what is the 10th term of an arithmetic sequence?
Un = U1 + (n – 1)d
We need to determine what the first term is...
d = and a5 = 15
U5 = U1 + (5 – 1)4 = 15
U1 = –1
U10 = –1 + (10 – 1)4
U10 = 35

5. Which can be simplified to:
To find the sum of an arithmetic series, we can use summation notation. First term is a1 or u1 and an or un is the last term
Which can be simplified to:

6. Example: Find the sum of the first 100 terms of the arithmetic sequence 1, 2, 3, 4, 5, 6, ...=