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4-7 Arithmetic Sequences

4-7 Arithmetic Sequences. Objective: To identify and extend patterns in sequences and represent in function notation. 4-7 Arithmetic Sequences. Getting Ready on page 276. Solve IT. 4-7 Arithmetic Sequences. A sequence is an ordered list of numbers that often forms a pattern.

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4-7 Arithmetic Sequences

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  1. 4-7 Arithmetic Sequences Objective: To identify and extend patterns in sequences and represent in function notation

  2. 4-7 Arithmetic Sequences • Getting Ready on page 276. Solve IT

  3. 4-7 Arithmetic Sequences • A sequence is an ordered list of numbers that often forms a pattern. • Each number in the list is called a term of a sequence. • Some sequences can be modeled with a function rule so that you can extend the sequence to any value.

  4. 4-7 Arithmetic Sequences • Example 1: What are next two terms? • A. 5, 8, 11, 14 . . . • B. 2.5, 5, 10, 20 . . .

  5. 4-7 Arithmetic Sequences • An arithmetic sequence: the difference between consecutive is a constant term, which is called the constant difference. • Example 2: Is it an arithmetic sequence? • A. 3, 8, 13, 18 . . . • B. 6, 9, 13, 17 . . .

  6. 4-7 Arithmetic Sequences • Sequences are functions and the terms are the outputs of the function. A recursive formula is a fn rule that relates each term of a sequence after the first to the ones before it.

  7. 4-7 Arithmetic Sequences 7, 11, 15, 19 . . . Find the common difference: FIRST Write the recursive formula: Let n = term in sequence A(n) = the value of the nth term

  8. 4-7 Arithmetic Sequences 7, 11, 15, 19 . . . Let n = term in sequence A(n) = the value of the nth term Value of term 1 = A(1) = 7 Value of term 2 = A(2) = A(1) + 4 = 11 Value of term 3 = A(3) = A(2) + 4 = 15 Value of term 4 = A(4) = A(4) + 4 = 19 Value of term 2 = A(2) = A(1) + 4 = 11 Value of term n = A(n) = A(n-2) + 4

  9. 4-7 Arithmetic Sequences The formula for Arithmetic Sequences A(n) = A(1) + (n – 1) d Term number Common difference Term number First term

  10. 4-7 Arithmetic Sequences The formula for Arithmetic Sequences A(n) = A(1) + (n – 1) d Example 4: An online auction works as shown: Write a formula for it. Determine common difference: A(n) = What is 12th bid?

  11. 4-7 Arithmetic Sequences The formula for Arithmetic Sequences Example 5: An RECURSIVE formula is represented by: A(n) = A(n– 1) + 12 If the first term is 19, write explicit formula So A(1) = 19 and adding 12 is common difference A(n) = A(1) + (n – 1)d so substitute what you know A(n) = 19 + (n-1)12 Arithmetic formula

  12. 4-7 Arithmetic Sequences The formula for Arithmetic Sequences Example 6: An Arithmetic formula is represented by: A(n) = 32 + (n-1)22 So the first term is ? So common difference is? A(n) = A(n – 1) + d so substitute what you know A(n) = Recursive formula

  13. 4-7 Arithmetic Sequences HW p. 279 9 – 42 every third

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