11.3 – Geometric Sequences.

Slides:

Advertisements

Similar presentations

Geometric Sequences.

Advertisements

Warm-up Finding Terms of a Sequence

Geometric Sequences Section

Bellwork:  Determine whether each of the following is Arithmetic (something was added each time), Geometric ( something was multiplied each time), or.

A sequence is geometric if the ratios of consecutive terms are the same. That means if each term is found by multiplying the preceding term by the same.

11.3 – Geometric Sequences.

Geometric Sequences and Series

Section 7.2 Arithmetic Sequences Arithmetic Sequence Finding the nth term of an Arithmetic Sequence.

What are two types of Sequences?

Find each sum:. 4, 12, 36, 108,... A sequence is geometric if each term is obtained by multiplying the previous term by the same number called the common.

Geometric Sequences as Exponential Functions

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

Do you remember what an arithmetic sequence is?

Section Finding sums of geometric series -Using Sigma notation Taylor Morgan.

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)

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

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

ADD To get next term Have a common difference Arithmetic Sequences Geometric Sequences MULTIPLY to get next term Have a common ratio.

+ 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,...

May 1, 2012 Arithmetic and Geometric Sequences Warm-up: What is the difference between an arithmetic and geometric sequence? Write an example for each.

+ 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.

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

Sequences Arithmetic Sequence:

Geometric Sequences and Series

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

3.5 Arithmetic Sequences as Linear Functions

Arithmetic and Geometric Sequences

Geometric Sequences Part 1.

AKS 67 Analyze Arithmetic & Geometric Sequences

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

Module 1 Day 1 Evaluating Functions.

Recursive and Explicit Formulas for Arithmetic (Linear) Sequences

Unit 4 Part B GEOMETRIC SEQUENCES

Recursive and Explicit Formulas for Arithmetic (Linear) Sequences

How does the geometric sequence differ from the arithmetic sequence?

7-8 Notes for Algebra 1 Recursive Formulas.

Sequences and Series Arithmetic Sequences Alana Poz.

1.7 - Geometric sequences and series, and their

11.3 – Geometric Sequences.

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

Sequences and Series Day 7

Geometric Sequences Definitions & Equations

Geometric Sequences.

Geometric sequences.

Coordinate Algebra Day 54

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

10.2 Arithmetic Sequences and Series

Geometric Sequences.

Geometric Sequences.

Geometric sequences.

Recursive and Explicit Formulas for Arithmetic (Linear) Sequences

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.

Unit 3: Linear and Exponential Functions

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.

Chapter 9.1 Introduction to Sequences

Geometric Sequences and series

11.2 – Arithmetic Sequences

Questions over HW?.

Recursive and Explicit Formulas for Arithmetic (Linear) Sequences

Module 3 Arithmetic and Geometric 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 *Quiz Tomorrow*

Warm-Up Honors Algebra 2 9/7/18

Presentation transcript:

11.3 – Geometric Sequences

What is a Geometric Sequence? The ratio of a term to it’s previous term is constant. This means you multiply by the same number to get each term. This number that you multiply by is called the common ratio (r).

Ex: Determine if the sequence is geometric Ex: Determine if the sequence is geometric. If so, identify the common ratio 1, -6, 36, -216 yes. Common ratio=-6 2, 4, 6, 8 no. No common ratio

Important Formula for Geometric Sequence: Explicit Formula an = a1 * r n-1 Where: an is the nth term in the sequence a1 is the first term n is the number of the term r is the common ratio

Ex: Write the explicit formula for each sequence First term: a1 = 7 Common ratio = 1/3 Explicit: an = a1 * r n-1 a1 = 7(1/3) (1-1) = 7 a2 = 7(1/3) (2-1) = 7/3 a3 = 7(1/3) (3-1) = 7/9 a4 = 7(1/3) (4-1) = 7/27 a5 = 7(1/3) (5-1) = 7/81 Now find the first five terms:

Explicit Arithmetic Sequence Problem Find the 19th term in the sequence of 11,33,99,297 . . . an = a1 * r n-1 Start with the explicit sequence formula Find the common ratio between the values. Common ratio = 3 a19 = 11 (3) (19-1) Plug in known values a19 = 11(3)18 =4,261,626,379 Simplify

Find the 10th term in the sequence of 1, -6, 36, -216 . . . Let’s try one Find the 10th term in the sequence of 1, -6, 36, -216 . . . an = a1 * r n-1 Start with the explicit sequence formula Find the common ratio between the values. Common ratio = -6 a10 = 1 (-6) (10-1) Plug in known values a10 = 1(-6)9 = -10,077,696 Simplify