Algebra 4.6Arithmetic Sequences

Learning Targets

Language Goal Students will be able recognize and

extend an arithmetic sequence.Math Goal Students will be able to find a given

term of an arithmetic sequence.Essential Question How do you find a given term

without finding every term in between?

Warm-up

Homework Check

Homework Check

Vocabulary

Sequence:

Term:

Arithmetic Sequence:

Common Difference:

A list of numbers that often forms a pattern.

Each number in a sequence.

A sequence in which the terms differ by the same nonzero number.

The same nonzero number in which an arithmetic sequence differs. d

Example 1: Identifying Arithmetic Sequences

Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.

1. 12, 8, 4, 0, … 2. 1, 4, 9, 16, …

Example 1: Identifying Arithmetic Sequences

Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.

3. -4, -2, 1, 5, … 4. 4, 1, -2, -5, …

Example 1: Identifying Arithmetic Sequences

Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.

5. … 6. …

Example 1: Identifying Arithmetic Sequences

Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.

7. 9, 13, 17, 21, … 8. 10, 8, 5, 1, …

Example 2: Finding the nth Term of an Arithmetic Sequence

The nth term of an arithmetic sequence with common difference d and first term a1 is

an = a1 + (n – 1)d

Example 2: Finding the nth Term of an Arithmetic Sequence

Find the indicated term of each arithmetic sequence.

1. 22nd term: 5, 2, -1, -4, … 2. 15th term: a1= 7; d = 3

Example 2: Finding the nth Term of an Arithmetic Sequence

Find the indicated term of each arithmetic sequence.

3. 60th term: 11, 5, -1, -7, … 4. 12th term: a1=4.2; d = 1.4

Example 2: Finding the nth Term of an Arithmetic Sequence

Find the indicated term of each arithmetic sequence.

5. 16th term: 4, 8, 12, 16, … 6. 25th term: a1= -5; d = -2

Example 3: Word Problems

The odometer on a car reads 60,473. Every day, the car is driven 54 miles. What is the odometer reading 20 days later?

Example 3: Word Problems

Each time a truck stops, it drops off 250 pounds cargo. It started with a load of 2000 pounds. How much does the load weigh after the fifth stop?

Example 3: Word Problems

A bag of cat food weighs 18 pounds. Each day, the cats are fed 0.5 pound of food. How much does the bag of cat food weigh after 30 days?

Lesson Quiz