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Algebra II Honors—Day 69

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Warmup Solve and check: Find the next four terms of this arithmetic sequence: 207, 194, 181,... Find the indicated term of this arithmetic sequence:

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Warmup Check both solutions!!!

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Warmup Find the next four terms of this arithmetic sequence: 207, 194, 181,... What is the common difference?? (194-207=-13 and 181-194=-13, so d=-13) 207, 194, 181, 168, 155, 142, 129 -13

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Warmup Find the indicated term of this arithmetic sequence:

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Today Finish up Arithmetic Sequences and Series Essential Question/New Material Homework

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Essential Questions What is an arithmetic series and how is it calculated? What is a geometric sequence? What is a geometric series, and how is it calculated?

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UPPER BOUND (NUMBER) LOWER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE) Sigma Notation n (Index of summation)

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An arithmetic series is a series associated with an arithmetic sequence. The sum of the first n terms: OR

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Find the sum of the first 100 natural numbers. 1 + 2 + 3 + 4 + … + 100

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Find the sum of the first 14 terms of the arithmetic series 2 + 5 + 8 + 11 + 14 + 17 +…

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Find the sum of the series

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12.2 – Geometric Sequences and Series

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Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY To get next term Arithmetic Series Sum of Terms Geometric Series Sum of Terms

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Vocabulary of Sequences (Universal) Recursive Formula: a n+1 =a n (r) Explicit Formula

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Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 – 2 vs. 9/2 – 3… not arithmetic

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1/2 x 9 NA 2/3

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Find two geometric means between –2 and 54 -2, ____, ____, 54 -2 54 4 NA x The two geometric means are 6 and -18, since –2, 6, -18, 54 forms a geometric sequence

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-3, ____, ____, ____

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x 9 NA

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x 5

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*** Insert one geometric mean between ¼ and 4*** *** denotes trick question 1/4 3 NA

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1/2 7 x

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Section 12.3 – Infinite Series

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1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2, 4, 8, …Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1 Sequence Type Series

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Find the sum, if possible:

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Homework Handout on Arithmetic and Geometric Sequences/Series—Due Tuesday for a grade

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SEQUENCES AND SERIES Arithmetic. Definition A series is an indicated sum of the terms of a sequence. Finite Sequence: 2, 6, 10, 14 Finite Series:2.

SEQUENCES AND SERIES Arithmetic. Definition A series is an indicated sum of the terms of a sequence. Finite Sequence: 2, 6, 10, 14 Finite Series:2.

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