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Class Motto

Class Motto. What are we doing? WE DO WHAT WE HAVE TO DO, SO WE CAN DO WHAT WE WANT TO DO. Arithmetic Sequences & Series Part 2. Today’s Objective: SWBAT write arithmetic sequences SWBAT specific terms of a sequence SWBAT define arithmetic sequences using recursive formulas.

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Class Motto

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  1. Class Motto • What are we doing? WE DO WHAT WE HAVE TO DO, SO WE CAN DO WHAT WE WANT TO DO

  2. Arithmetic Sequences & SeriesPart 2 Today’s Objective: SWBAT write arithmetic sequences SWBAT specific terms of a sequence SWBAT define arithmetic sequences using recursive formulas

  3. Arithmetic Sequences & Series Defined… • Recursive formula: expresses each new term based on the preceding term. • The rule for writing an recursive formula is: • an = an-1 + d, where a1 is given • a1 = 1st term • n = term we are looking for • d = common difference

  4. Arithmetic Sequences & Series Problem in Action #1 cont… For the sequence, write an recursive formula: 5, 9, 13, 17, …. • an = an-1 + d • a1 = 1st term: 5 • n = term we are looking for: unknown (n) • d = common difference: 4 • an = an-1+ 4 , a1 = 5

  5. Arithmetic Sequences & Series Problem in Action #1 cont… For the sequence, find a5, a6 using the recursive formula created: 5, 9, 13, 17, …. an = an-1 + d a1 = 1st term: 5 n = term we are looking for: unknown (n) d = common difference: 4 an = an-1 + 4 , a1 = 5 • a5 = a5-1 + 4 • a5 = a4 + 4 • a5 = 17+ 4 • a5 = 21 • a6 = a5 + 4 = 21 + 4 = 25

  6. Arithmetic Sequences & Series Problem in Action #1 cont… Use the recursive formula to calculate the next 3 terms: an = an-1 + 4 a1 = 1st term: 9 n = next 3 terms (2, 3, 4) d = common difference: 4 an = an-1 + 4 , a1 = 9 9, …. • a2 = a2-1 + 4 = a1 + 4 = 9 + 4= 13 • a 3= a3-1 + 4 = a2 + 4 = 13 + 4 = 17 • a4 = a4-1 + 4 = a3 + 4 = 17 + 4 = 21

  7. Arithmetic Sequences & Series Try This: For the sequence, 9, 20, 31, 42, …. • Write a recursive formula: an = an-1 + d • Label: a1, d, and n • Find a5 and a6 term using the formula created:

  8. Arithmetic Sequences & Series Try This: For the sequence, 9, 20, 31, 42, …. • Write a recursive formula: an = an-1 + d • Label: a1, d, and n • an = an-1 + 11 , a1 = 9 • Find a5 and a6 term using the formula created: • an = an-1 + 11 , a1 = 9 • a5 = a4 + 11 • a5 = 42 + 11 = 53 • a6 = 53 + 11 = 64

  9. Today’s Independent Practice • Students will complete the following:Skill Practice: pg. 94 • For the following problems: #22-25 • Write an recursive formula:an = an-1 + d • Find a5 , a6 , and a7 term using the formula created: • Complete pg. 95 #34-37

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