1. 8-2 Analyzing Arithmetic Sequences and Series

2. Arithmetic Sequences
A sequence of numbers is called an arithmetic sequence if the difference of any two consecutive terms is constant. This difference is called a common difference d.
Examples of arithmetic sequence

3. The nth term of an arithmetic sequence with the first term and common difference d is given by:
EXAMPLE 1

4. EXAMPLE 2
Is this an arithmetic sequence?
a) -9, -2, 5, 12, 19
(-2) – (-9) = 5 – (-2) = 12 – 5 = 19 – 12 = 7
Yes, it is an arithmetic sequence with a common difference of 7.
d = 7
b) 23, 15, 9, 5, 3
No, because there is
no common difference.

5. EXAMPLE 3 Find the formula for the nth term of
this arithmetic sequence:
25, 21, 17, 13, 9,…

6. EXAMPLE 4

7. Sum of finite arithmetic series
The sum of the first n terms of an arithmetic series is
Proof

8. EXAMPLE 5
Find the first and last terms:
Find the sum:

9. EXAMPLE 6 There is a house of cards as shown in the picture
Write a rule for the number of cards in the nth
row when the top row is row 1.
How many cards do you need to make a house of cards
with 9 rows?

10. The End