Aim: What is the geometric sequence?

Slides:

Advertisements

Similar presentations

Unit 6: Sequences & Series

Advertisements

4.7: Arithmetic sequences

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.

Arithmetic Sequences Notes. Definitions Sequence is a set of numbers arranged in a particular order. Term is one of the set of numbers in a sequence.

Series NOTES Name ____________________________ Arithmetic Sequences.

Geometric Sequences Section

Sequences. Mathematical Patterns Suppose each student in your math class has a phone conversation with every other member of the class. What is the minimum.

11.3 – Geometric Sequences.

Geometric Sequences and Series

Aim: What are the arithmetic series and geometric series? Do Now: Find the sum of each of the following sequences: a)

Lesson 4-4: Arithmetic and Geometric Sequences

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

12-1 Arithmetic Sequences and Series. Sequence- A function whose domain is a set of natural numbers Arithmetic sequences: a sequences in which the terms.

Ch.9 Sequences and Series

12.2: Analyze Arithmetic Sequences and Series HW: p (4, 10, 12, 14, 24, 26, 30, 34)

Arithmetic Sequences Explicit Formula.

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

11.5 = Recursion & Iteration. Arithmetic = adding (positive or negative)

Arithmetic Sequence Chapter 2, lesson C. IB standard Students should know Arithmetic sequence and series; sum of finite arithmetic series; geometric sequences.

Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.

Aim: What is the arithmetic sequence? Do Now: Find the first four terms in the sequence whose n th term is 4n + 3. HW: p.256 # 4,5,6,8,10,12,16,18,19,20.

Patterns and Sequences

Sequences & Series. Sequences  A sequence is a function whose domain is the set of all positive integers.  The first term of a sequences is denoted.

9.1 Notes Geometric Mean. 9.1 Notes Arithmetic mean is another term that means the same thing as average. The second do now question could have been,

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.

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…

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

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

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

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

Series & Sequences Piecewise Functions

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

1.2 Geometric Sequences and Series Warm-up (IN) 1.Find the sum of the arithmetic series: a …+460 b. Learning Objective: to understand what.

Sequences & Series. Sequence: A function whose domain is a set of consecutive integers. The domain gives the relative position of each term of the sequence:

2, 4, 8, 16, … 32 Exercise. 2, 4, 6, 8, … Exercise 10.

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)

Algebra 1 Functions 5 Evaluate and write geometric sequences Recall: arithmetic sequence t n = t 1 + (n-1)d A sequence is geometric if the ratio “r” of.

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.

Geometric Sequence Sequences and Series. Geometric Sequence A sequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512,...

+ 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.

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.

Warm Up Week 4 ( 2, 5 ) and ( 14, 1 ) 1) What is the midpoint?

Unit 9: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

Given an arithmetic sequence with

Chapter 13: Sequences and Series

Sequences Arithmetic Sequence:

4-7 Arithmetic Sequences

Geometric and arithmetic sequences

Geometric Sequences and Series

Aim: What is the arithmetic sequence?

Arithmetic and Geometric Means

Aim: What is the arithmetic and geometric sequence?

11-3 Geometric Sequences Hubarth Algebra II.

AKS 67 Analyze Arithmetic & Geometric Sequences

Aim: What is the geometric series ?

11.3 – Geometric Sequences.

11.3 – Geometric Sequences.

Geometric Sequences.

Geometric Sequences.

Notes Over 11.5 Recursive Rules

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

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

Module 3 Arithmetic and Geometric Sequences

SECTIONS 9-2 and 9-3 : ARITHMETIC &

4-7 Arithmetic Sequences

Homework Questions.

Presentation transcript:

Aim: What is the geometric sequence? Do Now: Find the first 5 numbers in a sequence whose nth term is 2n. 2, 4, 8, 16, 32 HW: p.269 # 4,6,8,16,18,20,28,30,32,34

This sequence is called a geometric sequence 2, 4, 8, 16, 32 Each term of the sequence is formed by multiplying the pervious term by 2, or we could say that the ratio of each term to the previous term is a constant,2. This sequence is called a geometric sequence A geometric sequence is a sequence such that for all n, there is a constant r such that The constant r is called common ratio The common ratio of the sequence 2,4,8,16,32 is 2.

The recursive formula of geometric sequence is an = a1rn-1 When the geometric sequence is written in terms of a1 and r, the terms of a geometric sequence are: The recursive formula of geometric sequence is an = a1rn-1 Is the sequence 4,12,36,108,324,… a geometric sequence? The ratio of any two consecutive terms is always 3, therefore the sequence is a geometric sequence with common ratio = 3

Write the first five terms of the geometric sequence whose first term is a1 = 3 and whose common ratio is r = 2. a1 = 3, a2 = 6, a3 = 12, a4 = 24, a5 = 48 Find the 12th term of the geometric sequence whose first three terms are 5, 15, 45. . .

Find the 15th term of the geometric sequence whose first term is 20 and whose common ratio is 1.05. 39.599 The 4th term of a geometric sequence is 125, and the 10th term is 125/64. Find the 14th term. 125/1024

We already knew the arithmetic mean between any two terms is the average of the two terms. The geometric mean between any two terms is the square root of the product of the two terms. The geometric mean between 4 and 100 is

Find four geometric means between 5 and 1215 This question can be rewritten as if the 1st and 6th terms of a geometric sequence are 5 and 1215. find the 2nd, 3rd, 4th and 5th terms. We want to find the missing terms in the sequence 5, a2, a3, a4, a5, 1215. use the formula to determine the common ratio r 15, 45, 135 and 405