WARM UP/GO OVER IT: 15 MINUTES ANNOUNCEMENTS: 1 MINUTE HOMEWORK: 10 MINUTES GEOMETRIC SEQUENCES: 30 MINUTES CLASS WORK: 20 MINUTES MIDTERM RETURN/CLOSURE:

Slides:

Advertisements

Similar presentations

Unit 6: Sequences & Series

Advertisements

Warm up 1. Determine if the sequence is arithmetic. If it is, find the common difference. 35, 32, 29, 26, Given the first term and the common difference.

Warm-up Finding Terms of a Sequence

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.

Geometric Sequences Section

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.

Sec 11.3 Geometric Sequences and Series Objectives: To define geometric sequences and series. To define infinite series. To understand the formulas for.

Warm-Up 1.Grab a worksheet off the stool. 2.Complete all of the odds.

Geometric Sequences and Series

Lesson 4-4: Arithmetic and Geometric Sequences

WARM UP/GO OVER IT: 15 MINUTES ANNOUNCEMENTS/NEW UNIT: 1 MINUTE PATTERNS/MAKE YOUR OWN: 10 MINUTES EXPLICIT AND RECURSIVE: 14 MINUTES ARITHMETIC 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.

Mid-Chapter Test Review

Explicit, Summative, and Recursive

Introduction to Geometric Sequences and Series

Explicit & Recursive Formulas.  A Sequence is a list of things (usually numbers) that are in order.  2 Types of formulas:  Explicit & Recursive Formulas.

What are two types of Sequences?

Warm Up Finish your open notes quiz from yesterday. When you come in, I will return your quiz to you. Remember, you may use your 4 pages of notes and the.

8.6 Geometric Sequences.

13.3 Arithmetic and Geometric Series and Their Sums

Review for the Test Find both an explicit formula and a recursive formula for the nth term of the arithmetic sequence 3, 9, 15,……… Explicit Formula ______________________________.

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.

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

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

Unit 5 – Series, Sequences, and Limits Section 5.2 – Recursive Definitions Calculator Required.

Geometric Sequences & Series

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

Do you remember what an arithmetic sequence is?

Warm Up 1. First: state whether each series below is arithmetic or not. 2. Then, find the sum of each series: a.

Objective: 1. After completing activity 1, mod With 90% accuracy 3. -Identify sequences as arithmetic, geometric, or neither -Write recursive formulas.

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)

Sequences and Series Explicit, Summative, and Recursive.

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

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 (

+ 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.

Lesson 11.4 Geometric Sequences. Warm Up ½ A geometric sequence is a sequence in which the ratio of successive terms is the same number, r, called.

Sequences A sequence is an ordered list of numbers that often form a pattern. Each number in the list is called a term of the sequence. A wooden post-and-rail.

8-5 Ticket Out Geometric Sequences Obj: To be able to form geometric sequences and use formulas when describing geometric sequences.

Bellwork 1) Find the fifth term of the sequence: a n = 3n + 2 a n = 3n + 2 2) Find the next three terms of the sequence 3, 5, 7, 9, 11, … Explain your.

Warm up Write the exponential function for each table. xy xy

Warm-Up #34 Thursday, 12/10. Homework Thursday, 12/10 Lesson 4.02 packet Pg____________________.

Recursive vs. Explicit. Arithmetic Sequence – Geometric Sequence – Nth term – Recursive – Explicit –

Geometric Sequences and Series

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

AKS 67 Analyze Arithmetic & Geometric Sequences

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

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

11.3 – Geometric Sequences.

Sequences Day 6 Happy Thursday!!.

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

Arithmetic Sequence A sequence of terms that have a common difference between them.

Warm Up Find the next 3 terms in the following sequence and describe the pattern 1) 3, 7, 11,15, 19, _______, _______, _______ Pattern:_________________.

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

Geometric Sequences and series

Arithmetic Sequence A sequence of terms that have a common difference between them.

Questions over HW?.

Arithmetic Sequence A sequence of terms that have a common difference (d) between them.

Warm Up Write the first 4 terms of each sequence:

Warm-up *Quiz Tomorrow*

Warm-Up Honors Algebra 2 9/7/18

Presentation transcript:

WARM UP/GO OVER IT: 15 MINUTES ANNOUNCEMENTS: 1 MINUTE HOMEWORK: 10 MINUTES GEOMETRIC SEQUENCES: 30 MINUTES CLASS WORK: 20 MINUTES MIDTERM RETURN/CLOSURE: 10 MINUTES AFM Unit 5 – Sequences and Series

Warm Up 1. Write the explicit and recursive formula for the following sequences: 4, 21, 38,… -4.5, -9.5, -14.5,… 2. Find the 6 th term of each of the following sequences, and tell whether the formula given is explicit or recursive. a 1 = 10, a n = a n – 1 – 7 a n = 15n – 9 3. Find the common difference of the arithmetic sequence for which a 1 = 75 and a 38 = 56.5

Announcements You have until THIS (Friday) afternoon to complete any and all make up work for this quarter. This includes finishing your midterm and make up tests. I will be here today after school. You will get your midterm grades back at the end of the period. We will stop about 6 minutes before the bell rings so you can get them back and look through them.

HOMEWORK: Check your answers 1. Yes, d = Yes, d = Yes, d = Yes, d = Yes, d = Yes, d = , 3, 10, 17, 24 and , -135, -235, -335, -435 and , -11.3, -13.4, -15.5, and , 2.375, 2.875, 3.375, and

Homework – You give ME the answers!

Yesterday: Arithmetic Sequences What do you remember about arithmetic sequences? What was the formula for the recursive formula? What was the formula for the explicit formula?

Today: Geometric Sequences Geometric Sequences – a few examples below to see if you can figure out what makes a geometric sequence a geometric sequence

Geometric Sequence The ratio between successive terms is constant. In other words…Each term is multiplied or divided by the same number. Example: -3, -15, -75, -375

Are the following sequences geometric?

Common Ratio The number that each term is multiplied or divided by to get the next term. Represented by the variable “r” To find it: divide any term by the previous term. Example: What is the common ratio of the sequence below?

Find the common ratios of the sequences below. 8, -2, 1/2 … 4, 11, 30.25… W + 3, 2w + 6, 4w + 12…

Find the common ratio and use it to generate the next 4 terms of each sequence below. - ¼, ½, -1, … 0.5, 0.75, 1.125, …

Recursive Formula Gives you… The first term (a 1 ) What to multiply the previous term by Remember, a n – 1 means “the one that came before it”

Geometric Recursive Formula a n = a n – 1 r

Generate the first 4 terms of the sequences given by the formulas below: a 1 = 8, a n = a n – a 1 = 2x, a n = a n – 1 5

Recursive  Explicit Let’s say you have a geometric sequence where a 1 = 3 and r = 4 first terma1a1 a1a1 a1a1 3 Second terma2a2 Third term Fourth term Fifth term Sixth term

GEOMETRIC EXPLICIT FORMULA a n = a 1 r n – 1

Writing Formulas Write an explicit and recursive formula for finding the nth term of the geometric sequence below. 2, 25, 312.5,…..

You try the next 3. 36, 12, 4,… -2, 10, -50,… 4, 8, 16,…

Nth terms Find the 27th term of the geometric sequence 189, 151.2, …

You try two. Find a 9 for 60, 30, 15… Find a 6 for 7, 14, 28,…

Arithmetic vs. Geometric

Practice Time Complete the problems on the worksheet I give you. You may work with your neighbors. Whatever you do not finish is homework!

Homework Finish class work!

Midterm Return Each part of each question was worth an equal amount. There was no partial credit. Your answer was either right or wrong. That means there were 58 total points. Your total correct out of 58 is where I got the percentage.