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Sequences A sequence is an ordered list of numbers. Term – Each number in a sequence is called a term. Examples: 1, 2, 3, 4, 5 1st 2nd 3rd 4th 5th term term term term term 2, 4, 8, 16, 32 1st 2nd 3rd 4th 5th term term term term term Three Types of Sequences •Arithmetic sequence – each term is found by adding the same number to the previous term. •Geometric sequence – each term is found by multiplying the previous term by the same number. •Neither – each term is found by adding or multiplying the previous term by a different number Examples: 1, 2, 4, 7, 11, 16 Rule: Add 1, 2, 3, 4, 5, … 1, 2, 6, 24, 120, 720 Rule: Multiply by 2, 3, 4, 5, 6, … Describe the pattern of each sequence and tell whether it is arithmetic or geometric: • 8, 13, 18, 23, … Rule: Add 5 to each term - Arithmetic • 1, 4, 16, 64, … Rule: Multiply each term by 4 – Geometric • 3, 6, 10, 15, … Rule: Add 3, 4, 5, …to each term - Neither Determine the next three terms in each sequence: • 0, 9, 18, 27, ___, ___, ___ 36, 45, 54 • 200, 202, 206, 212, ___, ___, ___ 220, 230, 242 • 4, 12, 36, 108, ___, ___, ___ 324, 972, 2916 Create a sequence of four terms in which the first term is 30 and the next terms are found by multiplying by 3. Create a sequence of four terms in which the first term is 25 and the next terms are found by choosing your own rule.