Recognizing Patterns and Sequences

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Presentation transcript:

Recognizing Patterns and Sequences Lesson 1

Sequence A sequence is a pattern of an ordered list of elements (numbers, figures in a picture, letters etc.) A term in the sequence is an individual item / element of the list. Examples: 3, 5, 7, 9… J, F, M, A, M, J, J, The “…” indicates that the pattern continues. Infinite sequences continue on forever (…) Finite sequences terminate (stop)

A sequence is a function whose: 3 5 7 9 3 5 7 9 A sequence is a function whose: -domain is a subset of integers (the natural #s) -range are the terms themselves (the actual number or item in the list) Think: the input/x-value/domain is 1, 2, 3, 4, etc for how far in the list it is the output/y-value/range are the actual numbers in the pattern

Term Notation We use subscript to identify each term of the sequence starting at 1: a1 is used to identify the 1st term in the sequence. a12 is used to identify the 12th term in the sequence. an is used to identify the nth term in the sequence. Example sequence 1, 2, 4, 8, 16, 32 So a1 = 1, a2 = 2, a3 = 4, a4 = 8 etc. Mean Same Thing

Describe the pattern in the sequence Example 1: 2, 8, 32, 128, … Multiply by 4 each time first term a1=2 Example 2: 555, 55.5, 5.55, .555, … Divide by 10 each time first term a1=555 List the next 3 terms in the sequence Example 3: 5, 2.5, 0, … Add -2.5 (like subtract 2.5) 5, 2.5, 0, -2.5, -5, -7.5 Example 4: 32, 16, 8, 4,… Multiply by ½ (like divide by 2) 32, 16, 8, 4, 2, 1, ½