1. Ch.9 Sequences and Series
Section 2 – Arithmetic Sequences

2. Definition: Arithmetic Sequence
A sequence where the difference between consecutive terms is constant. This difference is the common difference.
a, a + d, a + 2d, a +3d,…

3. Formulas
Recursive:
initial condition
recursive formula
Explicit:

4. EXamples Is the sequence an arithmetic sequence? 1.) 3,6,9,12,15,…
2.) 1,4,9,16,25,…

5. EXamples
What is the 100th term of the sequence beginning with 6, 11, …?

6. EXample
What are the second and third terms of the arithmetic sequences 100, __, __, 82,…

7. Definition: Arithmetic Mean
The average of two numbers and .
In an arithmetic sequence, the middle term of any three consecutive terms is the arithmetic of the other two terms.

8. EXample
What is the missing term of the arithmetic sequence …, 15, __, 59, …?

9. EXample
The numbers of seats in the first 13 rows in the section of an arena form an arithmetic sequence. Row 1 has 14 seats, row 2 has 16 seats. How many seats are in row 13?