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**Recursive & Explicit Formulas**

January 5 – 7, 2010

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**Closed/Explicit Formula**

January 6, 2010 Closed/Explicit Formula

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Warm Up (1/6) You can burn 5 calories a minute from walking. Which set could represent the range of calories burned when walking between 1 and 5 minutes? a. {1,2,3,4,5} c. {5} b. {5,10,15,20,25} d. {1,5} Which sequence is not a linear function? a. 1,2,3… c. 2,5,8… b. 1,4,9 d. -12,-8,-4… Given the first term in the sequence below, use the recursive formula given to find the next four terms of the sequence. a. 15,12,9,6 c. -3,6,12,18 b. 18,15,12,9 d. 18,12,6,-3

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**Explicit Formula for the nth term of a sequence**

nth term 1st term # of common the term difference trying to find Find the indicated term.

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**What is the 23rd term of the following sequence?**

5, 12, 19, 26, … a1 = 5; d = 7

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**You Try! Find the 9th term in the following sequence: 9, 2, -5, -12,…**

a1 = 9; d = -7

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Practice 13, 25, 37, 49,… find the 25th term a1 = 13; d = 12

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**Write the equation for the nth term**

17, 28, 39, 50, … a1 = 17; d = 11 7, 4, 1, -2, … a1 = 7; d = -3

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**Sequence 1: -4, 1, 6, 11, … Find common difference (d)**

Write the sequence in explicit /closed form: tn = t1 + (n-1)d tn = (n-1)(5) Find the 10th term --- Find the 25th term ---

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**Sequence 2: 8, 5, 2, -1, … Find common difference (d)**

Write the sequence in explicit/closed form: tn = t1 + (n-1)d tn = 8 + (n-1)(-3) Find the 10th term --- Find the 25th term ---

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**Sequence 3: -2, -4, -6, -8, … Find common difference (d)**

Write the sequence in explicit/closed form: tn = t1 + (n-1)d tn = (n-1)(-2) Find the 10th term --- Find the 25th term ---

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**Sequence 4: 4, 7, 10, 13, … Find common difference (d)**

Write the sequence in explicit/closed form: tn = t1 + (n-1)d tn = 4 + (n-1)(13) Find the 10th term --- Find the 25th term ---

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Homework Textbook p. 145; and 45 ALL

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