Warm UpState the pattern for each step.

• 3, 6, 9, 12, 15, 18, 21, 24, …

• 25, 20, 15, 10, 5, 0, -5, -10, …

• -21, 3, 27, 51, 75, 99, 123, …

ARITHMETIC SEQUENCES

Arithmetic Sequence

An arithmetic sequence is defined as a sequence in which there is a common difference between consecutive terms.

26, 21, 16, 11, 6, . . .

Common Difference = 5

Is the given sequence arithmetic? If so, identify the common difference.

1. 2, 4, 8, 16, …2. 4, 6, 12, 18, 24, …3. 2, 5, 7, 12, … 4. 48, 45, 42, 39, …5. 1, 4, 9, 16, …6. 10, 20, 30, 40, …

Arithmetic Sequence Formula

The “nth” number in the sequence.

Ex. a5 is the 5th number in the

sequence.

The 1st number in the sequence.

The same as the n in an. If you’re

looking for the 5th number in the

sequence, n = 5.

The common difference.

an = a1 + (n – 1) • d

Example 1:

Given the sequence -4, 5, 14, 23, 32, 41, 50,…, find the 14th term.

an = a1 + (n – 1) • d

Example 2:

Given the sequence 6, 10, 14, 18, 22, 26,…, find the 17th term.

an = a1 + (n – 1) • d

Example 3:

Given the sequence 81, 80.5, 80, 79.5, 70,…, find the 9th term.

an = a1 + (n – 1) • d

Example 4:

Given the sequence 79, 75, 71, 67, 63,…, find the term number that is -169.

an = a1 + (n – 1) • d

Example 5:

Suppose you are saving up for a new gaming system. You have 100 dollars this year, and you plan to add 33 dollars each of the following years. How much money will you have in 7 years?

an = a1 + (n – 1) • d

Arithmetic Mean

• Used to find the missing term of an arithmetic sequence

• Add the numbers and divide by two.

Find the missing term of the arithmetic sequence.

84, ____, 110

Find the missing term of the arithmetic sequence.

24, ____, 57