Advanced Math Topics Mrs. Mongold

Slides:

Advertisements

Similar presentations

Daily Check Find the first 3 terms of the following sequence:

Advertisements

Geometric Sequences.

Chapter 1: Number Patterns 1.6: Geometric Sequences

Lesson 4-4: Arithmetic and Geometric Sequences

Mid-Chapter Test Review

Patterns and Sequences

Math 3 - Module 6 Honors Topics.

Homework Questions. Geometric Sequences In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.

Arithmetic and Geometric

Arithmetic and Geometric Sequences Finding the nth Term 2,4,6,8,10,…

Algebra II Chapter : Use Recursive Rules with Sequences and Functions HW: p (4, 10, 14, 18, 20, 34)

Coordinate Algebra Arithmetic and Geometric Sequences Learning Target: Students can use the explicit formula to find the n th term of a sequence.

Lesson 4-6: Geometric Series Advanced Math Topics Mrs. Mongold.

11.2 & 11.3: Sequences What is now proven was once only imagined. William Blake.

Arithmetic and Geometric Sequences. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 1. 7, 13, 19, 25, …2.

+ Lesson 3B: Geometric Sequences + Ex 1: Can you find a pattern and use it to guess the next term? A) 3, 9, 27, … B) 28, 14, 7, 3.5,... C) 1, 4, 9, 16,...

+ 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.

Geometric Sequence: each term is found by multiplying the previous term by a constant.

13.1 Arithmetic and Geometric Sequences Explicit Formulas.

Geometric and arithmetic sequences

Lesson 3A: Arithmetic Sequences Ex 1: Can you find a pattern and use it to guess the next term? A) 7, 10, 13, 16,... B) 14, 8, 2, − 4,... C) 1, 4, 9,

Bellwork 1) 11, 7, 3, -1,… a) Arithmetic, Geometric, or Neither? b) To get the next term ____________ 1) 128, 64, 32, 16,… a) Arithmetic, Geometric, or.

Recursive vs. Explicit. Arithmetic Sequence – Geometric Sequence – Nth term – Recursive – Explicit –

Unit 4: Sequences & Series 1Integrated Math 3Shire-Swift.

Geometric Sequences Types of sequences When you are repeatedly adding or subtracting the same value to/from the previous number to get the next.

Arithmetic and Geometric Sequences.

Sequences Arithmetic Sequence:

4-7 Arithmetic Sequences

Geometric and arithmetic sequences

Geometric Sequences and Series

Arithmetic and Geometric Sequences

Warm up f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9

Arithmetic Sequences and Geometric Sequences

Geometric Sequences Part 1.

AKS 67 Analyze Arithmetic & Geometric Sequences

Arithmetic & Geometric Sequences

Patterns & Sequences Algebra I, 9/13/17.

Module 1 Day 1 Evaluating Functions.

Arithmetic & Geometric Sequences

4.7: Arithmetic sequences

Warm up Write the exponential function for each table. x y x

12.5 Recursive Rules with Sequences & Functions

11.3 – Geometric Sequences.

11.3 Geometric Sequences.

Geometric Sequences.

Coordinate Algebra Day 54

Arithmetic and geometric sequences

Warm up f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9

Arithmetic Sequences:

Warm Up Find the next 3 terms in the following sequence and describe the pattern 1) 3, 7, 11,15, 19, _______, _______, _______ Pattern:_________________.

Homework Questions.

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

EOC Practice Alex started a business making bracelets. She sold 30 bracelets the first month. Her goal is to sell 6 more bracelets each month than she.

Write the recursive and explicit formula for the following sequence

Welcome Is the number 27 a term in the sequence represented by the explicit formula an = 4n – 1? Is the number 97 a term in the sequence represented by.

Homework: Explicit & Recursive Definitions of

Questions over HW?.

Module 3 Arithmetic and Geometric Sequences

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*

Warm up Yes; common difference = -0.2 No; common ratio = -1

Arithmetic & Geometric Sequences

Geometric Sequences and Series

Presentation transcript:

Advanced Math Topics Mrs. Mongold Geometric Sequences Advanced Math Topics Mrs. Mongold

Reminder: Arithmetic Sequence Definition: Sequence in which the difference between any term and the term before it is a constant. i.e. you are adding or subtracting the same number each time Example: 2, 4, 6, 8, … You are adding 2 to each term to get the next 10, 9, 8, 7, … You are subtracting 1 from each term to get the next

Common Difference Definition: Example: The value of an – an-1 2, 4, 6, 8, … 4 – 2 = 2 6 – 4 = 2 8 – 6 = 2 d= 2

Geometric Sequence Definition: Example: Sequence in which the ratio of any term to the term before it is a constant. i.e. each term is multiplied or divided by the same number Example: 2, 4, 8, 16, … You multiply the previous term by 2 to get the next number 81, 27, 9, 3, … You divide each term by 3 to get the next number

Common Ratio The value of an divided by an-1 Example: 2, 4, 8, 16, … 4/2 = 2 8/4 = 2 16/8 = 2 So common ratio r =2 If the pattern is dividing the common ratio is a fraction!!!

Geometric Sequence 0.05, 0.25, 1.25, 6.25, … Explicit Formula an=a1rn-1 Pattern is previous term times 5 so r = 5 an=.05 (5)n-1 Recursive Formula an=(an-1)r Pattern is previous term times 5 so r = 5 an =(an-1)5 an=5(an-1)

Examples 1,-5, 25, -125, … -4, -8/3, -16/9, -32/27…

More Examples a1 = 4, r=3

More Examples a1 = 8, r= ½

More Examples a1 = 25, r= -5

More Examples

More Examples 100, 20, 4, 0.8, …

More Examples 1, 3, 6, 10, …

More Examples 12, 17, 22, 27, …

More Examples 0, 1, -1, 0, 1, -1 …

More Examples 25, 22, 19, 16, …

More Examples

Homework Arithmetic Sequences HW #2 Geometric Sequences HW #3