Sequences and Series Learn what is meant by a geometric sequence Learn how to find the nth term of a geometric sequence.

Slides:

Advertisements

Similar presentations

Infinities 2 sequences and series. 9: :00 Geometric Sequences 11: :00 Sequences, Infinity and ICT 14: :30 Quadratic Sequences.

Advertisements

11.3: Geometric Sequences & Series

Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?

Warm Up Find the geometric mean of 49 and 81..

Determine whether the sequence 6, 18, 54, is geometric. If it is geometric, find the common ratio. Choose the answer from the following :

11.3 Geometric Sequences.

Notes Over 11.3 Geometric Sequences

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

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.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 5.7 Arithmetic and Geometric Sequences.

Arithmetic Sequences and Series

Notes Over 11.4 Infinite Geometric Sequences

Geometric Sequences and Series Unit Practical Application “The company has been growing geometrically”

13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…

Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….

GEOMETRIC SEQUENCES These are sequences where the ratio of successive terms of a sequence is always the same number. This number is called the common.

Sequences Revision Learning Objective:  Arithmetic Sequences  Geometric Sequences  Nth terms  Sums.

13.4 Geometric Sequences and Series Example:3, 6, 12, 24, … This sequence is geometric. r is the common ratio r = 2.

Geometric Sequences & Series

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

CHAPTER Continuity Series Definition: Given a series   n=1 a n = a 1 + a 2 + a 3 + …, let s n denote its nth partial sum: s n =  n i=1 a i = a.

Geometric Series. In a geometric sequence, the ratio between consecutive terms is constant. The ratio is called the common ratio. Ex. 5, 15, 45, 135,...

Sequences & Series: Arithmetic, Geometric, Infinite!

Series A series is the sum of the terms of a sequence.

Review of Sequences and Series

Thursday, March 8 How can we use geometric sequences and series?

9.3 Geometric Sequences and Series. 9.3 Geometric Sequences A sequence is geometric if the ratios of consecutive terms are the same. This common ratio.

12.3 – Analyze Geometric Sequences and Series. Geometric Sequence: Ratio of any term to the previous term is constant Common Ratio: Ratio each term is.

9.3: Geometric Sequences and Series Objectives: Find the n th term and geometric mean Find the sum of n terms ©2002 Roy L. Gover (

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,...

Honors Precalculus Day 3 Section 11.3 Geometric Sequences The end of new material…BOO!!! 3/12/2016.

Geometric Sequences. Warm Up What do all of the following sequences have in common? 1. 2, 4, 8, 16, …… 2. 1, -3, 9, -27, … , 6, 3, 1.5, …..

Geometric Sequence – a sequence of terms in which a common ratio (r) between any two successive terms is the same. (aka: Geometric Progression) Section.

1.2 Cont. Learning Objective: to continue to find terms of sequences and then to find the sum of a geometric series. Warm-up (IN) 1.Give the first 4 terms.

Section 8.4 Mathematical Induction. Mathematical Induction In this section we are going to perform a type of mathematical proof called mathematical induction.

13.3 Arithmetic and Geometric Series and Their Sums Finite Series.

9.3 Geometric Sequences and Series. Common Ratio In the sequence 2, 10, 50, 250, 1250, ….. Find the common ratio.

Geometric Sequences and Series Notes 9.2. Notes 9.2 Geometric Sequences  a n =a 1 r n-1 a 1 is the first term r is the ratio n is the number of terms.

Section 1: Sequences & Series /units/unit-10-chp-11-sequences-series

S ECT. 9-2 SERIES. Series A series the sum of the terms of an infinite sequence Sigma: sum of.

Holt McDougal Algebra 2 Geometric Sequences and Series Holt Algebra 2Holt McDougal Algebra 2 How do we find the terms of an geometric sequence, including.

11.3 Geometric Sequences & Series

Series and Convergence (9.2)

nth or General Term of an Arithmetic Sequence

13.3 – Arithmetic and Geometric Series and Their Sums

11.3 Geometric sequences; Geometric Series

Warm-up Problems Consider the arithmetic sequence whose first two terms are 3 and 7. Find an expression for an. Find the value of a57. Find the sum of.

Infinite Geometric Series

Geometric Sequences Chapter 7.

1.7 - Geometric sequences and series, and their

For the geometric series below, what is the limit as n →∞ of the ratio of the n + 1 term to the n term?

11.3 – Geometric Sequences.

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.

12.3 Geometric Sequences & Series

Finite Geometric Series

10.2 Arithmetic Sequences and Series

Find the sums of these geometric series:

Sequences and Series Geometric series..

Arithmetic Sequences.

If the sequence of partial sums converges, the series converges

Warm up 1. One term of a geometric sequence is a5 = 48. The common ratio is r = 2. Write a rule for the nth term. 2. Find the sum of the geometric.

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.

Geometric Sequences and series

Section 2 – Geometric Sequences and Series

Geometric Sequence Skill 38.

Section 12.3 Geometric Sequences; Geometric Series

11.5 Arithmetic and Geometric Series

Presentation transcript:

Sequences and Series Learn what is meant by a geometric sequence Learn how to find the nth term of a geometric sequence

Paper folding If you fold a piece of paper in half 50 times, how thick would it be?? Lets assume it is 0.1mm thick to start with… 0.1 x 2 x 2 x 2 x 2 x 2….. Surely there is a quicker way!!! 0.1 x 2 50 = 113,000,000,000,000mm = 113,000,000km Don’t try this at home!!

Geometric Sequences In general… u n =u 1 x r n-1 1 st termCommon ratio From the formula booklet

Example 1 Find the 20 th term of the sequence 2, 6, 18, 54…. u n =u 1 x r n-1 u 1 = 2r = 3n = 20 u 20 =2 x 3 19 u 20 =2,324,522,934

Activity 6 questions

Activity hp?ref=188

Plenary =7773 Pairs Game Converging Series Sum of n terms