Arithmetic & Geometric Sequences

Slides:



Advertisements
Similar presentations
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.
Advertisements

Geometric Sequences Section
2-3 Geometric Sequences Definitions & Equations
 Find the next three terms in each sequence:  5, 15, 45, 135, _____, _____, _____  0.5, 2, 8, 32, _____, _____, _____  -32, 16, -8, 4, _____, _____,
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
Sequences and Series It’s all in Section 9.4a!!!.
Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 5.7 Arithmetic and Geometric Sequences.
12.2: Analyze Arithmetic Sequences and Series HW: p (4, 10, 12, 14, 24, 26, 30, 34)
Chapter 8: Sequences and Series Lesson 1: Formulas for Sequences Mrs. Parziale.
Today in Precalculus Notes: Sequences Homework Go over quiz.
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.
Algebra II Chapter : Use Recursive Rules with Sequences and Functions HW: p (4, 10, 14, 18, 20, 34)
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 5 Number Theory and the Real Number System.
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)
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.
Arithmetic and Geometric Sequences.
Given an arithmetic sequence with
Chapter 13: Sequences and Series
Review Find the explicit formula for each arithmetic sequence.
Sequences Arithmetic Sequence:
8.1 Sequences.
Geometric Sequences.
Geometric Sequences and Series
Warm-up 1. Find 3f(x) + 2g(x) 2. Find g(x) – f(x) 3. Find g(-2)
Arithmetic and Geometric Sequences
Patterns and Sequences
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 8.1 Sequences.
Discrete Mathematics Lecture#14.
AKS 67 Analyze Arithmetic & Geometric Sequences
Arithmetic & Geometric Sequences
Patterns & Sequences Algebra I, 9/13/17.
Arithmetic & Geometric Sequences
7-8 Notes for Algebra 1 Recursive Formulas.
4.7: Arithmetic sequences
11.3 – Geometric Sequences.
11.3 – Geometric Sequences.
Geometric Sequences Definitions & Equations
11.3 Geometric Sequences.
Geometric Sequences.
Geometric sequences.
Section 5.7 Arithmetic and Geometric Sequences
Coordinate Algebra Day 54
Warm Up 1. Find 3f(x) + 2g(x) 2. Find g(x) – f(x) 3. Find g(-2)
4-7 Sequences and Functions
Geometric Sequences.
Arithmetic Sequences:
Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.
Geometric sequences.
Arithmetic Sequence A sequence of terms that have a common difference between them.
Module 3 Arithmetic and Geometric Sequences
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.
Arithmetic Sequence A sequence of terms that have a common difference between them.
Advanced Math Topics Mrs. Mongold
Questions over HW?.
Arithmetic Sequence A sequence of terms that have a common difference (d) between them.
Module 3 Arithmetic and Geometric Sequences
Sequence.
Geometric Sequences and Series
Lesson 6.7 Recursive Sequences
Presentation transcript:

Arithmetic & Geometric Sequences

Definitions Sequences are terms organized in a particular order. Arithmetic Sequence is a sequence with the difference between two consecutive terms constant. This difference is called the common difference. Geometric Sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.

Example of a sequence

Section 9.4 Guessing The Sequence Guess which sequence is arithmetic or geometric. 3, 8, 13, 18, 23, . . . 1, 2, 4, 8, 16, . . .

Group Work Card sorting activity

General General a10 a6

Practice Problems pg. 676 21-28 (part B only) 21. 6, 10, 14, 18…….. Find the tenth term. 25. 2, 6, 18, 54……… Find the eighth term.

Arithmetic Sequence Arithmetic definition: Pairs of successive terms that all have a common difference. Meaning: a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5,7,9,11,13,15… is an arithmetic progression with the common difference being 2.

Recursive formula: Each term from an arithmetic sequence can be obtained recursively from its preceding term by adding d: an=an-1+d

Example 1 Practice p676#21-24 Use the following sequnce to find: (a)Find the common difference (b) Find the tenth term (c ) find a recursive rule for the nth term (d) find the explicit rule for the nth term -6,-2,2,6,10….

Geometric Sequence A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. R is called the common ratio. Each term in a geometric sequence can be obtained recursively from its preceding term by multiplying by r:

Geometric Sequence Recursive Formula an=an-1*r