1. Chapter 11 Sequences and Series
Algebra 2
Chapter 11 Sequences and Series

2. 11-2 Arithmetic Sequences
WARMUP: Simplify:
-7 + (6 – 1)3
4 + (n – 1)(-2)
Evaluate if n = 50:
-3 + 4n
100 – (0.5)n
Solve the system:
6 = x + y
14 = x + 5y

3. 11-2 Arithmetic Sequences
Objective:
To find a formula for the nth term of an arithmetic sequence and to find specified terms of arithmetic sequences.

4. 11-2 Arithmetic Sequences
Say we have this arithmetic sequence:
3, 7, 11, 15, …
We have a common difference of d = 4
So the next few terms would be…
…, 15, 19, 23, …
What if we wanted to know the 105th term of the sequence?

5. 11-2 Arithmetic Sequences
Quick note about notation.
We designate the terms of the sequence from the previous example as follows:
t1 t2 t3 t4 t5 …
3, 7, 11, 15, 19, …
Therefore the 5th term is 19. The 3rd term is 11.

6. 11-2 Arithmetic Sequences
Look at initial example in book, p. 507.
(99 differences)

7. 11-2 Arithmetic Sequences
IMPORTANT!
In an arithmetic sequence with first term t1 and common difference d, the nth term (or general term) is given by

8. 11-2 Arithmetic Sequences
Examples:
Let’s go back to the sequence we started with:
3, 7, 11, 15, …
Find tn .
Find t17
Find t3

9. 11-2 Arithmetic Sequences
Notice that the equation for the nth term works for ANY term in the sequence. To check, see if t1 matches the first number in your sequence…

10. 11-2 Arithmetic Sequences
More examples:
Find a formula for the nth term of each sequence:
-1, 0, 1, 2, …
30, 20, 10, 0, …
-3, -10, -17, -24, …
-6, -1, 4, 9, …

11. 11-2 Arithmetic Sequences?
Arithmetic Mean:
A single arithmetic mean between two numbers is called the arithmetic mean. The arithmetic mean of the numbers a and b is

12. 11-2 Arithmetic Sequences
What is the arithmetic mean of:
-4 and 8
17 and 20

13. 11-2 Arithmetic Sequences
A tougher kind of arithmetic sequence problem:

14. 11-2 Arithmetic Sequences
More examples.

15. 11-2 Arithmetic Sequences
Homework: