# Algebra II Honors—Day 69. Warmup Solve and check: Find the next four terms of this arithmetic sequence: 207, 194, 181,... Find the indicated term of this.

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Algebra II Honors—Day 69

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

Warmup Check both solutions!!!

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

Warmup Find the indicated term of this arithmetic sequence:

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

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?

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

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

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

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

Find the sum of the series

12.2 – Geometric Sequences and Series

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

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

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

1/2 x 9 NA 2/3

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

-3, ____, ____, ____

x 9 NA

x 5

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

1/2 7 x

Section 12.3 – Infinite Series

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

Find the sum, if possible:

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

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