1. Arithmetic Sequences
Lesson 30

2. Objectives
HSF-BF.2: Write arithmetic sequences with an explicit formula, use them to model situations.

3. Arithmetic Sequence

4. Example; Arithmetic Sequence
Find the 12th term of the arithmetic sequence 20, 14, 8, 2, 4, ....
Step 1 Find the common difference: d = 14 – 20 = –6.
Step 2 Evaluate by using the formula.
an = a1 + (n – 1)d
General rule.
an = (n – 1)(-6)
Substitute in a1 and d
an = n + 6
Distribute
an = -6n + 26
Simplify
a12 = -6(12) + 26
Substitute 12 for n
a12 = –46
The 12th term is –46.

5. Example; Arithmetic Sequence
Find the 10th term of the arithmetic sequence 2, 14, 26, 38, 50, ....
Step 1 Find the common difference: d = 14 – 2 = 12.
Step 2 Evaluate by using the formula.
an = a1 + (n – 1)d
General rule.
an = 2 + (n – 1)(12)
Substitute in a1 and d
an = n - 12
Distribute
an = 12n - 10
Simplify
a10 = 12(10) - 10
Substitute 10 for n
a10 = 110
The 10th term is 110.

6. Example; Arithmetic Sequence
Find the 11th term of the arithmetic sequence.
-3, -5, -7, -9, …
Step 1 Find the common difference: d = -5 – -3 = –2.
Step 2 Evaluate by using the formula.
an = a1 + (n – 1)d
General rule.
an = -3 + (n – 1)(-2)
Substitute in a1 and d
an = n + 2
Distribute
an = -2n - 1
Simplify
a11 = -2(11) - 1
Substitute 11 for n
a11 = –23
The 11th term is –23.

7. Example; Arithmetic Sequence
A small business sells $20,000 worth of sports memorabilia during its first year. The owner of the business has set a goal of increasing annual sales by $15,000 each year for 19 years. Assuming that this goal is met, find the total sales during the first 20 years this business is in operation.
a1 = and d = 15,000
an = 20, ,000(n – 1)
an = 15,000n
This implies that the 20th term of the sequence is
a20 = 15,000(20)
a20 = 300,
a20 = 305,000.
Total sales in the 20th year is $305,000.

8. #30: Arithmetic Sequences
Questions?
Summarize Notes
Homework
Google Classroom
Quiz