New EQ: How are sequences like functions?

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Presentation transcript:

New EQ: How are sequences like functions? Math 1 10/6/11 New EQ: How are sequences like functions? Turn in homework – page 42 Pick up Calculator WARM-UP: Write the next 3 terms in the sequences below 1. 3, 6, 9, 12, … 2. 4, 10, 16, 22, … 3. 10, 8, 6, 4, 2, …

Go over homework pp. 42

SEQUENCE NOTES What's a sequence? Examples Notation A sequence is a list of numbers Any time you write numbers in a list format, you are creating a sequence What's a sequence? 1, 2, 3, 4, 5, ... 2, 4, 6, 8, 10, ... -3, -7, -11, ... Examples an n tells the number of the term n = 1, 2, 3, 4, 5, ... Notation

SEQUENCE NOTES A _____________ of a sequence is just a number that is in the sequence. Terms are identified by their location in the sequence. The 1st term in a sequence is called a1 The 5th term in a sequence is called a5 Arithmetic sequence: Common difference: (___)

SEQUENCE NOTES an = a(n – 1) + d Recursive formula: Examples: 1, 3, 4, 7, 9, … 2, 7, 12, 17, … 3, 0, -3, -6, …

Identify the 1st term and the difference Explicit formula: (Closed form) an = a1 + d(n – 1) Examples: 1, 3, 4, 7, 9, … 2, 7, 12, 17, … 3, 0, -3, -6, … Identify the 1st term and the difference Substitute into the formula Simplify

Guided Practice 3, 6, 9, 12, 15, … What’s a15? What’s a25?

Guided Practice 2) a1 = 6 and d = 2 What’s a4? What’s a24? What’s a94?

Guided Practice 3) a1 = 8 and a2 = 13

Assignment Complete pages 46