1. Arithmetic Sequences & Series
Mr. Peter Richard,
So bright that his mother calls him “sun” will teach you this series

2. Arithmetic Sequence:
The difference between consecutive terms is constant (or the same).
The constant difference is also known as the common difference (d).
(It’s also that number that you are adding everytime!)

3. Example: Decide whether each sequence is arithmetic.
5,11,17,23,29,…
11-5=6
17-11=6
23-17=6
29-23=6
Arithmetic (common difference is 6)
-10,-6,-2,0,2,6,10,…
-6--10=4
-2--6=4
0--2=2
2-0=2
6-2=4
10-6=4
Not arithmetic (because the differences are not the same)

4. ARITHMETIC SEQUENCE d= term – previous term 1. 0, -8, -16, -24,…
A sequence in which a constant d can be added to each term to get the next term. The constant d is called the common difference.
d= term – previous term
1. 0, -8, -16, -24,…
d = -8
d = -3
2. -3, -6, -9, -12 …
d = -1/2
3. 1, 1/2, 0, -1/2 …

5. Rule for an Arithmetic Sequence
an=a1+(n-1)d
A(n) = nth term
a = first term
n = term number
d = common difference

6. Finding Terms of a Sequence
Find the first, fifth, and tenth terms of the sequence that has the rule
A(n) = 12 + (n – 1)(-2)
First term: A(1) = 12 + (1 – 1)(-2)
= 12
Fifth term: A(5) = 12 + (5 – 1)(-2)
= (-2) = 4
Tenth term: A(10) = 12 + (10 – 1)(-2)
= (-2) = -6

7. Assignment Quiz: Page 294 # 16, 22, 24, 26, 28 Homework: # 13, 23, 25, 27, 29