LEQ: How do you evaluate or find explicit formulas for arithmetic sequences?

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Presentation transcript:

LEQ: How do you evaluate or find explicit formulas for arithmetic sequences?

 A formula which describes any term in a sequence in terms of its position in the sequence.  For an Arithmetic Sequence: The n th term a n of an arithmetic sequence with first term a 1 and constant difference d is given by the explicit formula a n = a 1 + (n – 1)d.

 Find the 40 th term of the arithmetic sequence 74, 67, 60, 53, 46,… First write an explicit formula that represents the sequence: a 1 = 74 and d = -7, therefore a n = 74 + (n – 1)(-7) Substitute 40 for n: a 40 = 74 + (40 – 1)(-7) Simplify: a 40 = (-7) a 40 = 74 + (-273) a 40 = -199 The 40 th term is -199

 The first row in the auditorium has 15 seats in it. Each subsequent row has 3 more seats than the row in front of it. If the last row has 78 seats, how many rows are in the auditorium? Constant-increase situation…arithmetic sequence with t 1 = 15 and d = 3. t n = 15 + (n - 1)3 Last row has 78 seats, therefore t n = = 15 + (n – 1)3 63 = (n – 1)3 21 = n – 1 22 = n The auditorium has 22 rows

 Lesson Master 3-8A #1, 6, 11

 Pgs #1-7, 9-11, 13-19, 21, 22