13.2 Arithmetic & Geometric Sequences Today’s Date: 5/1/14.

Slides:



Advertisements
Similar presentations
I can identify and extend patterns in sequences and represent sequences using function notation. 4.7 Arithmetic Sequences.
Advertisements

4.7: Arithmetic sequences
11.3 – Geometric Sequences.
Lesson 4-4: Arithmetic and Geometric Sequences
Geometric Sequences and Series
Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.
Homework Questions. Number Patterns Find the next two terms, state a rule to describe the pattern. 1. 1, 3, 5, 7, 9… 2. 16, 32, 64… 3. 50, 45, 40, 35…
Today in Precalculus Notes: Sequences Homework Go over quiz.
Patterns and Sequences
F—06/11/10—HW #79: Pg 663: 36-38; Pg 693: odd; Pg 671: 60-63(a only) 36) a(n) = (-107\48) + (11\48)n38) a(n) = – 4.1n 60) 89,478,48562) -677,985,854.
12.2 & 12.5 – Arithmetic Sequences Arithmetic : Pattern is ADD or SUBTRACT same number each time. d = common difference – If add: d positive – If subtract:
Homework Questions. Geometric Sequences In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.
Homework Questions. Number Patterns Find the next two terms, state a rule to describe the pattern. 1. 1, 3, 5, 7, 9… 2. 16, 32, 64… 3. 50, 45, 40, 35…
13.4 Geometric Sequences and Series Example:3, 6, 12, 24, … This sequence is geometric. r is the common ratio r = 2.
Acc. Coordinate Algebra / Geometry A Day 36
Geometric Sequences & Series
Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.
Algebra II Chapter : Use Recursive Rules with Sequences and Functions HW: p (4, 10, 14, 18, 20, 34)
12.2, 12.3: Analyze Arithmetic and Geometric Sequences HW: p (4, 10, 12, 18, 24, 36, 50) p (12, 16, 24, 28, 36, 42, 60)
4.2B Geometric Explicit and Recursive Sequences
Arithmetic and Geometric Sequences. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 1. 7, 13, 19, 25, …2.
Review of Sequences and Series
11.3 – Geometric Sequences. What is a Geometric Sequence?  In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called.
+ 8.4 – Geometric Sequences. + Geometric Sequences A sequence is a sequence in which each term after the first is found by the previous term by a constant.
Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2.
Warm up Write the exponential function for each table. xy xy
Arithmetic and Geometric Sequences.
Given an arithmetic sequence with
Review Find the explicit formula for each arithmetic sequence.
4-7 Arithmetic Sequences
Geometric Sequences and Series
Warm-up 1. Find 3f(x) + 2g(x) 2. Find g(x) – f(x) 3. Find g(-2)
Warm up f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9
Lesson 13 – 2 Arithmetic & Geometric Sequences
Section 8.1 Sequences.
AKS 67 Analyze Arithmetic & Geometric Sequences
7-8 Notes for Algebra 1 Recursive Formulas.
Sequences and Series Arithmetic Sequences Alana Poz.
4.7: Arithmetic sequences
11.3 – Geometric Sequences.
Warm up Write the exponential function for each table. x y x
11.3 – Geometric Sequences.
Geometric Sequences Skill 50.
Geometric Sequences.
Coordinate Algebra Day 54
Warm Up 1. Find 3f(x) + 2g(x) 2. Find g(x) – f(x) 3. Find g(-2)
Geometric Sequences.
Notes Over 11.5 Recursive Rules
Warm up f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9
Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.
Arithmetic Sequence A sequence of terms that have a common difference between them.
Homework Questions.
Warm Up.
Geometric Sequences A geometric sequence is a list of numbers with a common ratio symbolized as r. This means that you can multiply by the same amount.
Module 3 Arithmetic and Geometric Sequences
Write the recursive and explicit formula for the following sequence
Classwork: Explicit & Recursive Definitions of
Homework: Explicit & Recursive Definitions of
Arithmetic Sequence A sequence of terms that have a common difference between them.
Questions over HW?.
Arithmetic Sequence A sequence of terms that have a common difference (d) between them.
8.5 Using Recursive Rules with Sequences
Module 3 Arithmetic and Geometric Sequences
4-7 Arithmetic Sequences
1.6 Geometric Sequences Geometric sequence: a sequence in which terms are found by multiplying a preceding term by a nonzero constant.
Warm Up Write the first 4 terms of each sequence:
Warm-up *Quiz Tomorrow*
Geometric Sequences and Series
Lesson 6.7 Recursive Sequences
Warm-Up Honors Algebra 2 9/7/18
Presentation transcript:

13.2 Arithmetic & Geometric Sequences Today’s Date: 5/1/14

Arithmetic sequence (defined recursively) A sequence a 1, a 2, a 3, … if there is a constant d for which a n = a n–1 + d for n > 1 (defined explicitly) the general term is a n = a 1 + (n – 1)d d is the common difference d = a n – a n–1 Ex 1) Determine if the sequence is arithmetic. If yes, name the common difference. a)20, 12, 4, –4, –12, …yesd = –8 b)9.3, 9.9, 10.5, 11.1, 11.7, …yesd = 0.6 Ex 2) Create your own arithmetic sequence with common difference of –1.5 (share a few together) Ex 3) Find the 102 nd term of the sequence 5, 13, 21, 29, … a 1 = 5a 102 = 5 + (102 – 1)(8) d = 8 = = 813

The graph of a sequence is a set of points – NOT a continuous curve If we know two terms of a sequence, we can find a formula. Ex 4) In an arithmetic sequence, a 5 = 24 and a 9 = 40. Find the explicit formula. (write what we know) 24 = a 1 + (5 – 1)d 40 = a 1 + (9 – 1)d Solve the system: a 1 + 4d = 24 a 1 + 8d = 40 – 4d = –16a = 24 d = 4 a 1 = 8 a n = 8 + (n – 1)(4) or a n = 4 + 4n sequence continuous function – ––

If a 1, a 2, a 3, …, a k–1, a k is an arithmetic sequence, then a 2, a 3, …, a k–1 are arithmetic means between a 1 and a k. Ex 5) Find 3 arithmetic means between 9 and 29. 9, ___, ___, ___, 29 *this is a stream-lined way to solve* last – first # of commas Geometric Sequence (defined recursively) A sequence a 1, a 2, a 3, …if there is a constant r for which a n = a n–1 · r for n > 1 (defined explicitly) the general term is a n = a 1 r n–1 r is the common ratio

Ex 6) Create your own geometric sequence with common ratio r = –2. (share please) Ex 7) Find an explicit formula for the geometric sequence 4, 20, 100, 500, … and use it to find the ninth term. a 1 = 4

If a 1, a 2, a 3, …, a k–1, a k is a geometric sequence, then a 2, a 3, …, a k–1 are called geometric means between a 1 and a k. Ex 8) Locate 3 geometric means between 4 and , ___, ___, ___, 324 or 4, ___, ___, ___, 324 *stream-lined way to solve* # of commas –1236–108 A single geometric mean is called the geometric mean. (the signs must be the same) Ex 9) Find the mean proportional m (if it exists) between: a) –42 and –378b) 1 and –16 DNE

Homework #1302 Pg 687 #1–3, 11, 13, 14, 15, 18, 20, 23–25, 28–30, 32, 34, 35, 38 *There are several word problems in the homework – just make the sequence and apply the rules!