# Recursive vs Explicit Formulas in Calorie Burn  January's Warm Up explores the advantages and differences between using recursive and closed explicit formulas to calculate calories burned while exercising.

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## About Recursive vs Explicit Formulas in Calorie Burn

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1. Recursive & Explicit Formulas January 5 – 7, 2010

2. January 6, 2010 Closed/Explicit Formula

3. Warm Up (1/6) 1. 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} 2. Which sequence is not a linear function? a. 1,2,3… c. 2,5,8… b. 1,4,9 d. -12,-8,-4… 3. 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

4. Explicit Formula for the nth term of a sequence nth term 1 st term # of common the term difference trying to find Find the indicated term.

5. What is the 23 rd term of the following sequence? • 5, 12, 19, 26, … • a 1 = 5; d = 7

6. You Try! • Find the 9 th term in the following sequence: 9, 2, -5, -12,… a 1 = 9; d = -7

7. Practice 1 3 , 2 5 , 3 7 , 4 9 , … f i n d t h e 2 5 t h t e r m a 1 = 1 3 ; d = 1 2

8. Write the equation for the nth term • 17, 28, 39, 50, … a 1 = 17; d = 11 • 7, 4, 1, -2, … a 1 = 7; d = -3

9. Sequence 1: -4, 1, 6, 11, … • Find common difference (d) • Write the sequence in explicit /closed form: t n = t 1 + (n-1)d t n = -4 + (n-1)(5) • Find the 10th term --- • Find the 25th term ---

10. Sequence 2: 8, 5, 2, -1, … Find common difference (d) Write the sequence in explicit/closed form: t n = t 1 + (n-1)d t n = 8 + (n-1)(-3) Find the 10th term --- Find the 25th term ---

11. Sequence 3: -2, -4, -6, -8, … Find common difference (d) Write the sequence in explicit/closed form: t n = t 1 + (n-1)d t n = -2 + (n-1)(-2) Find the 10th term --- Find the 25th term ---

12. Sequence 4: 4, 7, 10, 13, … Find common difference (d) Write the sequence in explicit/closed form: t n = t 1 + (n-1)d t n = 4 + (n-1)(13) Find the 10th term --- Find the 25th term ---

13. Homework Textbook p. 145; 39-42 and 45 ALL