WARM UP State the pattern for each set.

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Presentation transcript:

WARM UP State the pattern for each set. 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

Definition: Arithmetic Sequence A sequence in which there is a common difference (d) between consecutive terms. d= 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 term 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 term in the sequence, n = 5. The “nth” term in the sequence. ex. a5 is the 5th term.

Example 1: an = a1 + (n – 1) • d Given the sequence -4, 5, 14, 23, 32, 41, 50,…, find the 14th term. Given the sequence 6, 10, 14, 18, 22, 26,…, find the 17th term. Given the sequence 81, 80.5, 80, 79.5, 79,…, find the 9th term.

Given the sequence 79, 75, 71, 67, 63,…, find the term that has a value of -169.

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

Try this! Write a formula for the following sequences. b) The first term is 3 and the common difference is -21 The second term is 8 and the common difference is 3