Warm Up State the pattern for each step.

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Presentation transcript:

Warm Up State 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. Common Difference = 5

Is the given sequence arithmetic? If so, identify the common difference. 2, 4, 8, 16, … 4, 6, 12, 18, 24, … 2, 5, 7, 12, … 48, 45, 42, 39, … 1, 4, 9, 16, … 10, 20, 30, 40, …

Arithmetic Sequence Formula The 1st number in the sequence. The common difference. an = a1 + (n – 1) • d The same as the n in an. If you’re looking for the 5th number in the sequence, n = 5. The “nth” number in the sequence. Ex. a5 is the 5th number in the sequence.

Example 1: an = a1 + (n – 1) • d Given the sequence -4, 5, 14, 23, 32, 41, 50,…, find the 14th term.

Example 2: an = a1 + (n – 1) • d Given the sequence 6, 10, 14, 18, 22, 26,…, find the 17th term.

Example 3: an = a1 + (n – 1) • d Given the sequence 81, 80.5, 80, 79.5, 70,…, find the 9th term.

Example 4: an = a1 + (n – 1) • d Given the sequence 79, 75, 71, 67, 63,…, find the term number that is -169.

Example 5: an = a1 + (n – 1) • d 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?

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