Geometric Sequences.

Slides:

Advertisements

Similar presentations

Introduction Geometric sequences are exponential functions that have a domain of consecutive positive integers. Geometric sequences can be represented.

Advertisements

9-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

A geometric sequence is a list of terms separated by a constant ratio, the number multiplied by each consecutive term in a geometric sequence. A geometric.

Lesson 4-8 Example Example 3 What is the volume of the triangular prism? 1.Use the Pythagorean Theorem to find the leg of the base of the prism.

Geometric Sequences Section

Choi Geometric Sequence A sequence like 3, 9, 27, 81,…, where the ratio between consecutive terms is a constant, is called a geometric sequence. In a.

11.3 – Geometric Sequences.

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

11-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

9-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

Holt Algebra Geometric Sequences 11-1 Geometric Sequences Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

Algebra 1 Find the common ratio of each sequence. a. 3, –15, 75, –375,... 3–1575–375  (–5)  (–5)  (–5) The common ratio is –5. b. 3, ,,,...

Lesson 4-4: Arithmetic and Geometric Sequences

Chapter 8: Sequences and Series Lesson 1: Formulas for Sequences Mrs. Parziale.

Unit 6: Modeling Mathematics 3 Ms. C. Taylor. Warm-Up.

Solving Radical Equations

Standard # D Geometric Sequences GeometricSequence What if your pay check started at $100 a week and doubled every week. What would your salary.

Lesson 10-7 Geometric Sequences.

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

Aim: What is the geometric sequence?

Ch.9 Sequences and Series Section 3 – Geometric Sequences.

Aim: Geometric Sequence Course: Math Literacy Do Now: Aim: What are geometric sequences? Mrs. Gonzales sells houses and makes a commission of $3750 for.

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

11.3 – Geometric Sequences. What is a Geometric Sequence?  In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called.

+ 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.

Mathematical Patterns & Sequences. Suppose you drop a handball from a height of 10 feet. After the ball hits the floor, it rebounds to 85% of its previous.

Holt Algebra Solving Radical Equations Warm Up(Add to Hw) Solve each equation. 1. 3x +5 = x + 1 = 2x – (x + 7)(x – 4) = 0 5. x 2.

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.

Given an arithmetic sequence with

Arithmetic and Geometric sequence and series

9-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

Homework: Part I Find the next three terms in each geometric sequence.

Warm-up 1. Find 3f(x) + 2g(x) 2. Find g(x) – f(x) 3. Find g(-2)

Aim: What is the arithmetic and geometric sequence?

11-3 Geometric Sequences Hubarth Algebra II.

Section 11-5 Solving Radical Equations

Arithmetic & Geometric Sequences

Direct Variation Lesson 2-3.

Ratio & Proportions Practice

Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

9-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

Find the common difference of each sequence.

Sequences and Series Arithmetic Sequences Alana Poz.

11.3 – Geometric Sequences.

11.3 – Geometric Sequences.

11.3 Geometric Sequences.

Geometric Sequences.

Geometric Sequences.

Warm Up Solve each equation

Arithmetic Sequences.

Geometric Sequences.

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

Explicit formulas Sequences: Lesson 3.

9-1 Mathematical Patterns

Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

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.

Unit 3: Linear and Exponential Functions

Recursive & Explicit Processes

Homework: Explicit & Recursive Definitions of

Warm Up State the pattern for each step.

9-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

Questions over HW?.

Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

Warm-up L11-2 & L11-3 Obj: Students will be able to find the general term for arithmetic series.

Arithmetic & Geometric Sequences

11-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz

Presentation transcript:

Geometric Sequences

Geometric Sequences The ratio between consecutive terms is a constant. This constant ratio is called the common ratio (r).

Geometric Sequences Lesson 11-3 Additional Examples Is the given sequence geometric? If so, identify the common ratio. a. 1, –6, 36, –216, . . . 1, –6, 36, –216 –6 ÷ 1 = –6  –6 36 ÷ –6 = –6  –6 216 ÷ 36 = –6  –6 There is a common ratio of –6. This is a geometric sequence.

Geometric Sequences Lesson 11-3 Additional Examples (continued) b. 2, 4, 6, 8, . . . 2, 4, 6, 8 4 ÷ 2 = 2  2  3 2 6 ÷ 4 =  4 3 8 ÷ 6 = There is no common ratio. This is not a geometric sequence.

Geometric Sequence Formula

an = a1 • r n – 1 Use the explicit formula. Geometric Sequences Lesson 11-3 Additional Examples Suppose you have equipment that can enlarge a photo to 120% of its original size. A photo has a length of 10 cm. Find the length of the photo after 5 enlargements at 120%. You need to find the 6th term of the geometric sequence 10, 12, 14.4, . . . an = a1 • r n – 1 Use the explicit formula. a6 = 10 • 1.206 – 1 Substitute a1 = 10, n = 6, and r = 1.20. = 10 • 1.205 Simplify the exponent. 24.883 Use a calculator. After five enlargements of 120%, the photo has a length of about 25 cm.

Geometric Mean

geometric mean = 150,000 • 188, 160 Use the definition. Geometric Sequences Lesson 11-3 Additional Examples A family purchased a home for $150,000. Two years later the home was valued at $188,160. If the value of the home is increasing geometrically, how much was the home worth after one year? geometric mean = 150,000 • 188, 160 Use the definition. = 28,224,000,000 Multiply. = 168,000 Take the square root.

5. Find the missing term for the geometric sequence 3, , 48 . . . 12 Geometric Sequences Lesson 11-3 Lesson Quiz Is the given sequence geometric? If so, identify the common ratio and find the next two terms. 1. 1, 2, 6, 12, . . . 2. 2, 1, 0.5, 0.25, . . . no yes; 0.5; 0.125, 0.0625 3. –9, 81, –729, 6561, . . . yes; –9, –59,049, 531,441 4. Write the explicit formula for the geometric sequence for which a1 = 7 and r = . Then generate the first five terms. 1 3 an = 7 • ; 7, , , , 1 3 n – 1 7 9 27 81 5. Find the missing term for the geometric sequence 3, , 48 . . . 12