1 SS.01.4 - Recursion Formulas MCR3U - Santowski.

Slides:

Advertisements

Similar presentations

ELF.01.8 – Solving Word Problems Using Logarithms MCB4U - Santowski.

Advertisements

Warm-up Finding Terms of a Sequence

Warm-Up Identify each variable as the dependent variable or the independent for each of the following pairs of items the circumference of a circle.

Geometric Sequences Section

11.3 – Geometric Sequences.

Modeling Growth and Decay

SECTION 7.2 ARITHMETIC SEQUENCES. (a) 5, 9, 13, 17, 21,25 (b) 2, 2.5, 3, 3.5, 4, 4, (c) 8, 5, 2, - 1, - 4, - 7 Adding 4 Adding.5 Adding - 3 Arithmetic.

9/8/2015Math SL1 - Santowski1 Lesson 30 - Summation Notation & Infinite Geometric Series Math SL1 - Santowski.

Sequences and Series. Sequence - Is a relationship from the set of counting numbers (1, 2, 3...) to another set of numbers. Terms - The individual numbers.

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

1 Geometric Sequences MCR3U. 2 (A) Review A sequence is an ordered set of numbers. A sequence is an ordered set of numbers. An arithmetic sequence has.

Chapter 8: Sequences and Series Lesson 1: Formulas for Sequences Mrs. Parziale.

Mid-Chapter Test Review

Do Now Three years ago you bought a Lebron James card for $45. It has appreciated (gone up in value) by 20% each year since then. How much is worth today?

1 SS Solving Exponential Equations MCR3U - Santowski.

Math SL1 - Santowski 1 T1.1 – Sequences & Series Lesson 2 - Geometric Sequences 10/1/2015 T1.1 - Sequences & Series - Lesson 2.

Exponential Functions 1/30/2013. Warm-Up 3: A population of 25 bacteria doubles in size every week. a)Write an exponential function to model.

1 SS Simple Interest, Arithmetic Sequences and Linear Growth MCR3U – Mr. Santowski.

Warm up – Arithmetic Sequences Identify the next three terms and the common difference for the following sequences: 1.)0, 5, 10, 15, 20… 2.)74, 67, 60,

What are two types of Sequences?

ARITHMETIC SEQUENCES. (a) 5, 9, 13, 17, 21,25 (b) 2, 2.5, 3, 3.5, 4, 4, (c) 8, 5, 2, - 1, - 4, - 7 Adding 4 Adding.5 Adding - 3 Arithmetic Sequences.

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

Notes 9.4 – Sequences and Series. I. Sequences A.) A progression of numbers in a pattern. 1.) FINITE – A set number of terms 2.) INFINITE – Continues.

Patterns and Sequences

Column Sequences An Investigation Column Sequences Look carefully at the columns shown below and the way in which the numbers are being put into each.

Lesson 5.1.  You have used sequences and recursive rules to model geometric growth or decay of money, populations, and other quantities.  Recursive.

11/5/2015Math SL1 - Santowski1 T1.1 – Lesson 3 - Arithmetic & Geometric Series & Summation Notation Math SL1 - Santowski.

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

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

5-6 HISTORICAL AND EXPONENTIAL DEPRECIATION

1 SS Present Value of An Annuity MCR3U - Santowski.

Leonardo Pisano Fibonacci

Acc. Coordinate Algebra / Geometry A Day 36

Investigating Sequences and Series Arithmetic Sequences.

Warm-Up 7 Identify each variable as the dependent variable or the independent for each of the following pairs of items 1. the circumference of a circle.

Time to take your medicine! A patient is prescribed a 250 mg dose of an antibiotic to be taken every 8 hours for 3 days. The drug is both excreted and.

2/5/2013. Warm-Up 3 ( ) 1. Create a geometric sequence with 4 terms. 2. Write an explicit rule for the table: 3. How many bacteria would there.

Lesson 11.2 Arithmetic Sequences The slope and the common difference.

Recursive Formulas for Sequences Algebra II CP Mrs. Sweet

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

7-8: RECURSIVE FORMULAS Essential Skills: Use a recursive formula to list terms in a sequence Write recursive formulas for arithmetic and geometric sequences.

7-8 Geometric Sequences. Geometric Sequence Problem 1: Identifying Geometric Sequence Which of the following are geometric sequences? 20, 200, 2000,

+ 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.

Lesson 3A: Arithmetic Sequences Ex 1: Can you find a pattern and use it to guess the next term? A) 7, 10, 13, 16,... B) 14, 8, 2, − 4,... C) 1, 4, 9,

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

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

Over Lesson 7–7 5-Minute Check 1 Describe the sequence as arithmetic, geometric or neither: 1, 4, 9, 16, …? Describe the sequence as arithmetic, geometric,

Given an arithmetic sequence with

Warm up f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9

7-8 Notes for Algebra 1 Recursive Formulas.

11.3 – Geometric Sequences.

Sequences F.LE.1, 2, 5 F.BF.1, 2 A.SSE.1.a F.IF.1, 2, 3, 4

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

11.3 – Geometric Sequences.

Geometric Sequences Skill 50.

Geometric Sequences.

Notes Over 11.5 Recursive Rules

Warm up f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9

Grade 11 Functions (MCR3U)

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.

Write the recursive and explicit formula for the following sequence

Recursive & Explicit Processes

Homework: Explicit & Recursive Definitions of

Module 3 Arithmetic and Geometric Sequences

Warm Up Write the first 4 terms of each sequence:

Warm-Up Honors Algebra 2 9/7/18

Presentation transcript:

1 SS Recursion Formulas MCR3U - Santowski

2 (A) Review the formula for generating the terms of an arithmetic sequence is t n = a + (n - 1)d the formula for generating the terms of a geometric sequence is t n = ar n-1 these two formulas are referred to as explicit formulas

3 (B) An Investigation Into Recursion Formulas ex 1. A car worth $26,000 depreciates by 10% every year. (i) Determine the dollar amount of the depreciation at the end of year 1. (ii) Determine the residual value of the car at the end of year 1. What percent of the original selling price does this residual value represent? (iii) Repeat the above steps for year 2. (iv) Write the first five terms of the sequence that represents the residual value of the car at the end of each successive year. (v) Let t n represent any term in the sequence. Write an expression for the term previous to t n. (vi) Write a formula that can be used to generate the terms of the sequence that uses the previous term to calculate any term (except the first one)

4 (B) An Investigation Into Recursion Formulas ex 2. A pair of rabbits one month old is too young to produce more rabbits. But by the end of the second month, they produce a pair of rabbits, and a pair of rabbits every month after that. Each new pair of rabbits does the same thing, producing a pair of rabbits every month, starting after the second month. (i) Set up a chart or table to show how many rabbits there are each month until the start of the 9 th month. (ii) List the numbers of pairs of rabbits in order as the first 9 terms of a sequence. (iii) Is this sequence arithmetic or geometric? Is this a sequence? (iv) Describe in words and by a formula how to generate the next 5 terms of the sequence.

5 (C) Recursion Formulas in a recursive sequence, a new term is generated from the previous term or terms a recursive formula shows how to calculate each term from the previous term(s) a recursive formula has at least one known term

6 (D) Examples ex 1. Write the first four terms of the sequence t 1 = 2 and t n = 3t n ex 2. Write the first four terms of the sequence t 1 = -1, t 2 = 1, and t n = 2t n-2 - 3t n-1 ex 3. Write a recursive formula for the sequence 1, 2, -1, 3, -4, 7, -11 ex 4. Write a recursive formula for the sequence 2, 6, 18, 54 ex 5. Write a recursive formula for the sequence 1,2,4,7,11,16

7 (D) Examples ex 6. To relieve the pain of chromic headaches, my doctor prescribes 500 mg of aspirin every 6 hours. At this rate, only 26% of the aspirin remains in my body when I take the next dose. Determine the first 6 terms of the sequence representing the total amount of aspirin in my body when I take the next dose. Write the recursive formula and graph it. What happens to the aspirin in my body as I take more and more aspirin?

8 (E) Homework AW, page 36, Q6,7,9,10,11,12 Nelson Text, p32-34, Q1-3,5,6,8,9,11,13,16,17