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My Math 4 Volume 1 Common Core, Grade: 4 Publisher: McGraw-Hill
My math 4 volume 1 common core, title : my math 4 volume 1 common core, publisher : mcgraw-hill, isbn : 21150230, isbn-13 : 9780021150236, use the table below to find videos, mobile apps, worksheets and lessons that supplement my math 4 volume 1 common core., textbook resources.
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Subject: Mathematics
Age range: 11-14
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Last updated
6 July 2016
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it is very good but for the year 10, it does not start building up from a serquence, it goes straight to term.
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13.3E: Geometric Sequences (Exercises)
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13. Find the common ratio for the geometric sequence \(2.5, \quad 5, \quad 10, \quad 20, \ldots\)
14. Is the sequence \(4,16,28,40 \ldots\) geometric? If so find the common ratio. If not, explain why.
15. A geometric sequence has terms \(a_{7}=16,384\) and \(a_{9}=262,144 .\) What are the first five terms?
16. A geometric sequence has the first term \(a_{1}=-3\) and common ratio \(r=\frac{1}{2} .\) What is the \(8^{\text {th }}\) term?
17. What are the first five terms of the geometric sequence \(a_{1}=3, \quad a_{n}=4 \cdot a_{n-1} ?\)
18. Write a recursive formula for the geometric sequence \(1, \quad \frac{1}{3}, \quad \frac{1}{9}, \quad \frac{1}{27}, \ldots\)
19. Write an explicit formula for the geometric sequence \(-\frac{1}{5}, \quad-\frac{1}{15}, \quad-\frac{1}{45}, \quad-\frac{1}{135}, \ldots\)
20. How many terms are in the finite geometric sequence \(-5,-\frac{5}{3},-\frac{5}{9}, \ldots,-\frac{5}{59,049} ?\)
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Eureka Math Algebra 1 Module 3 Lesson 2 Answer Key
Engage ny eureka math algebra 1 module 3 lesson 2 answer key, eureka math algebra 1 module 3 lesson 2 example answer key.
Example 1. Consider Akelia’s sequence 5, 8, 11, 14, 17, …. a. If you believed in patterns, what might you say is the next number in the sequence? Answer: 20 (adding 3 each time)
b. Write a formula for Akelia’s sequence. Answer: A(n) = 5 + 3(n – 1)
c. Explain how each part of the formula relates to the sequence. Answer: To find each term in the sequence, you are adding 3 one less time than the term number. To get the 1st term, you add three zero times. To get the 2nd term, you add 3 one time. To get the 5th term, you add 3 four times.
d. Explain Johnny’s formula. Answer: His formula is saying that to find any term in the sequence, just add 3 to the term before it. For example, to find the 12th term, add 3 to the 11th term: A(12) = A(11) + 3. To find the 50th term, add 3 to the 49th term. To find the (n + 1)th term, add 3 to the nth term. It is critical that the value of the very first term be specified; we need it to get started finding the values of all the other terms.
Example 2. Consider a sequence given by the formula a n = a (n-1) -5, where a 1 = 12 and n ≥ 2. a. List the first five terms of the sequence. Answer: 12, 7, 2, -3, -8
b. Write an explicit formula. Answer: a n = 12-5(n-1) for n ≥ 1
c. Find a_6 and a_100 of the sequence. Answer: a 6 = -13 a 100 = -483
Eureka Math Algebra 1 Module 3 Lesson 2 Exercise Answer Key
Exercises 1–2
Exercise 1. Akelia, in a playful mood, asked Johnny: “What would happen if we change the ‘ + ’ sign in your formula to a ‘-’ sign? To a ‘×’ sign? To a ‘ ÷ ’ sign?” a. What sequence does A(n + 1) = A(n)-3 for n ≥ 1 and A(1) = 5 generate? Answer: Answer: 5, 2,-1, -4, …
b. What sequence does A(n + 1) = A(n) ⋅ 3 for n ≥ 1 and A(1) = 5 generate? Answer: 5, 15, 45, 135, …
c. What sequence does A(n + 1) = A(n) ÷ 3 for n ≥ 1 and A(1) = 5 generate? Answer: 5, \(\frac{5}{3}\), \(\frac{5}{9}\), \(\frac{5}{27}\), …
Exercise 2. Ben made up a recursive formula and used it to generate a sequence. He used B(n) to stand for the nth term of his recursive sequence. a. What does B(3) mean? Answer: It is the third term of Ben’s sequence.
b. What does B(m) mean? Answer: It is the m th term of Ben’s sequence.
c. If B(n + 1) = 33 and B(n) = 28, write a possible recursive formula involving B(n + 1) and B(n) that would generate 28 and 33 in the sequence. Answer: B(n) = B(n-1) + 5 (Note that this is not the only possible answer; it assumes the sequence is arithmetic and is probably the most obvious response students will give. If the sequence were geometric, the answer could be written as B(n + 1) = (\(\frac{33}{28}\))B(n).)
d. What does 2B(7) + 6 mean? Answer: It is 2 times the 7th term of Ben’s sequence plus 6.
e. What does B(n) + B(m) mean? Answer: It is the sum of the nth term of Ben’s sequence plus the m th term of Ben’s sequence.
f. Would it necessarily be the same as B(n + m)? Answer: No, adding two terms of a sequence is not the same as adding two of the term numbers and then finding that term of a sequence. Consider, for example, the sequence 1, 3, 5, 7, 9, 11, 13, …. Adding the 2nd and 3rd terms does not give you the 5th term.
g. What does B(17)-B(16) mean? Answer: It is the 17th term of Ben’s sequence minus the 16th term of Ben’s sequence.
Exercises 3–6
Exercise 3. One of the most famous sequences is the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, …. f(n + 1) = f(n) + f(n – 1), where f(1) = 1, f(2) = 1, and n ≥ 2 How is each term of the sequence generated? Answer: By adding the two preceding terms
Exercise 4. Each sequence below gives an explicit formula. Write the first five terms of each sequence. Then, write a recursive formula for the sequence. a. a n = 2n + 10 for n ≥ 1 Answer: 12, 14, 16, 18, 20 a n + 1 = a n + 2, where a 1 = 12 and n ≥ 1
b. a_n = (\(\frac{1}{2}\)) (n-1) for n ≥ 1 Answer: 1, \(\frac{1}{2}\), \(\frac{1}{4}\), \(\frac{1}{8}\), \(\frac{1}{16}\) a n + 1 = a n ÷ 2, where a 1 = 1 and n ≥ 1
Exercise 5. For each sequence, write either an explicit or a recursive formula. a. 1, -1, 1, -1, 1, -1, … Answer: a (n + 1) -a n , where a 1 = 1 and n≥1 or f(n) = (-1) (n + 1) , where n ≥ 1
b. \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{3}{4}\), \(\frac{4}{5}\), … Answer: f(n) = \(\frac{n}{n + 1}\) and n ≥ 1
Exercise 6. Lou opens a bank account. The deal he makes with his mother is that if he doubles the amount that was in the account at the beginning of each month by the end of the month, she will add an additional $5 to the account at the end of the month. a. Let A(n) represent the amount in the account at the beginning of the nth month. Assume that he does, in fact, double the amount every month. Write a recursive formula for the amount of money in his account at the beginning of the (n + 1)th month. Answer: A(n + 1) = 2A(n) + 5, where n ≥ 1 and A(1) is the initial amount
b. What is the least amount he could start with in order to have $300 by the beginning of the third month? Answer: A(3) = 2 ∙ A(2) + 5 A(3) = 2 ∙ [2 ∙ A(1) + 5] + 5 300 ≤ 2 ∙ [2 ∙ A(1) + 5] + 5 300 ≤ 4 ∙ A(1) + 15 71.25 ≤ A(1) The least amount he could start with in order to have $300 by the beginning of the third month is $71.25.
Eureka Math Algebra 1 Module 3 Lesson 2 Problem Set Answer Key
For Problems 1–4, list the first five terms of each sequence.
Question 1. a n + 1 = a n + 6, where a 1 = 11 for n ≥ 1 Answer: 11, 17, 23, 29, 35
Question 2. a n = a n-1 ÷ 2, where a 1 = 50 for n ≥ 2 Answer: 50, 25, 12.5, 6.25, 3.125
Question 3. f(n + 1) = -2f(n) + 8 and f(1) = 1 for n ≥ 1 Answer: 1, 6, -4, 16, -24
Question 4. f(n) = f(n-1) + n and f(1) = 4 for n ≥ 2 Answer: 4, 6, 9, 13, 18
For Problems 5–10, write a recursive formula for each sequence given or described below.
Question 5. It follows a plus one pattern: 8, 9, 10, 11, 12, Answer: f(n + 1) = f(n) + 1, where f(1) = 8 and n ≥ 1
Question 6. It follows a times 10 pattern: 4, 40, 400, 4000, …. Answer: f(n + 1) = 10f(n), where f(1) = 4 and n ≥ 1
Question 7. It has an explicit formula of f(n) = -3n + 2 for n ≥ 1. Answer: (n + 1) = f(n)-3, where f(1) = -1 and n ≥ 1
Question 8. It has an explicit formula of f(n) = -1(12) (n-1) for n ≥ 1. Answer: f(n + 1) = 12f(n), where f(1) = -1 for n ≥ 1
Question 9. Doug accepts a job where his starting salary is $30,000 per year, and each year he receives a raise of $3,000. Answer: D (n + 1) = D n + 3000, where D 1 = 30000 and n ≥ 1
Question 10. A bacteria culture has an initial population of 10 bacteria, and each hour the population triples in size. Answer: B (n + 1) = 3B n , where B 1 = 10 and n ≥ 1
Eureka Math Algebra 1 Module 3 Lesson 2 Exit Ticket Answer Key
Question 1. Consider the sequence following a minus 8 pattern: 9, 1, -7, -15, …. a. Write an explicit formula for the sequence. Answer: f(n) = 9-8(n-1) for n ≥ 1
b. Write a recursive formula for the sequence. Answer: f(n + 1) = f(n)-8 and f(1) = 9 for n ≥ 1
c. Find the 38th term of the sequence. Answer: f(38) = 9-8(37) = -287
Question 2. Consider the sequence given by the formula a(n + 1) = 5a(n) and a(1) = 2 for n ≥ 1. a. Explain what the formula means. Answer: The first term of the sequence is 2. Each subsequent term of the sequence is found by multiplying the previous term by 5.
b. List the first five terms of the sequence. Answer: 2, 10, 50, 250, 1250
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All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 7 Lesson 3 Sequences will give you a clear idea of the concepts. McGraw-Hill My Math Grade 4 Answer Key Chapter 7 Lesson 3 Sequences. Math in My World Example 1 Crystal starts reading her book on Monday. She reads 25 pages on the first day. Each day, she reads 25 pages.
Textbook: McGraw-Hill My Math Grade 4 Volume 1ISBN: 9780021150236. Use the table below to find videos, mobile apps, worksheets and lessons that supplement McGraw-Hill My Math Grade 4 Volume 1 book.
Use the table below to find videos, mobile apps, worksheets and lessons that supplement My Math 4 Volume 1 Common Core. My Math 4 Volume 1 Common Core grade 4 workbook & answers help online. Grade: 4, Title: My Math 4 Volume 1 Common Core, Publisher: McGraw-Hill, ISBN: 21150230.
Start with the first term of the sequence, which can be any number. Then, choose a common difference. This is the number we will add to each term in order to get the next term. For example, if we start with 5 and have a common difference of 3 , our sequence will be 5, 8, 11, 14, 17, 20 …. Practice with our Extend arithmetic sequences exercise.
The McGraw-Hill My Math Learning Solution provides an easy and flexible way to diagnose and fill gaps in understanding so that all students can meet grade-level expectations - and accelerate beyond: . Strong, equitable core instruction with actionable data Best-in-class resources and targeted instructional strategies Personalized, student-driven learning
an= 1/2n-1. Study with Quizlet and memorize flashcards containing terms like Identify the first five terms of the sequence in which a1 = 3 and an = 4an−1− 5 for n ≥ 2., Identify a possible explicit rule for the nth term of the sequence 9, 14, 19, 24, 29., Identify the first five terms of the sequence in which a1 = 1 and an = 3an −1 + 2 ...
Sequences & Series Notes & Homework Packet Lesson 1: Sequences Sequences are ordered lists of numbers. A sequence is formally defined as a function that has its domain the set of positive integers, i.e. {1, 2, 3, …, n}. Exercise 1: A sequence is defined by the equation a n = 2n - 1. (a) Find the first three terms of this sequence, denoted ...
LESSON/HOMEWORK. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY. Lesson 2 ... Unit 5 - Mid-Unit Quiz (After Lesson #3) - Form D ASSESSMENT. ANSWER KEY. EDITABLE ASSESSMENT. EDITABLE KEY. Add-on ... Practice with Arithmetic and Geometric Sequences RESOURCE. ANSWER KEY. EDITABLE RESOURCE. EDITABLE KEY.
sequence. the ordered arrangement that makes up a pattern. term. each number in a numeric pattern. unknown. an amount that is not known. expression. A mathematical phrase without an equal sign. Study with Quizlet and memorize flashcards containing terms like equation, input, nonnumeric pattern and more.
Description. In this lesson, students use their knowledge of sequences developed in Lessons 1 and 2 to differentiate between arithmetic and geometric sequences.
The first term in a sequence is 8 and the last term is 128 and there are 5 terms in the sequence. 23) If it is an arithmetic sequence, find the three middle terms. 24) If it is a geometric sequence, find the three middle terms. In a geometric sequence, t 3 = == = 9 999 and t 6 == = 1.125 = 1.125 25) Find t 7 26) Find t 9-2-
docx, 14.55 KB. docx, 42.24 KB. Variety of resources I've made to teach all aspects of sequences, from term-to-term rule, to position-to-term rule, to nth terms of linear and quadratic sequences. Use the PPT that best suits the ability of your class. There is also two really fun quizzes included which are great as an end of unit recap.
LESSON 3 Overview MATERIALS DIFFERENTIATION ©Curriculum Associates, LLC Copying is not permitted. LESSON 3 Work with Sequences of Transformations and Congruence 43b Pacing Guide Items marked with are available on the Teacher Toolbox. SESSION 1 Explore Sequences of Rigid Transformations and Congruence(35-50 min) • Start (5 min) • Try It (5-10 min)
February 10, 2020. 117 KB. Log in to Download. Log in to Write a Review. Sort by (Optional) Number Sequences and Patterns lesson plan template and teaching resources. 3 levels of number sequence/pattern work sheets.Homework sheets at different levels.
This suggested pacing for My Math, Grade 3 supports 1 day per lesson, and includes additional time for review and assessment, and remediation and differentiation for a total of 160 days. Use this pacing to help ensure in-depth coverage of all Grade 3 Common Core State Standards for Mathematics. Chapter 1 Place Value. 10 days.
Ready, Set, Go Homework: Sequences 3.7 . 3.8 Classroom Task: What Does It Mean? - A Solidify Understanding Task . Using rate of change to find missing terms in an arithmetic sequence . Ready, Set, Go Homework: Sequences 3.8 . 3.9 Classroom Task: Geometric Meanies - A Solidify and Practice Understanding Task. Using a constant ratio to find ...
Homework Helper A Story ofFunctions. 2015-16. M3. ALGEBRA I. Lesson 2 : 4Recursive Formulas for Sequences. Writing a Recursive Formula for a Sequence. 3. Write a recursive formula for the sequence that has an explicit formula 𝑓𝑓(𝑛𝑛) = 4𝑛𝑛−2 for 𝑛𝑛≥1. 𝒇𝒇(𝟏𝟏) = 𝟒𝟒(𝟏𝟏) −𝟐𝟐= 𝟐𝟐 ...
A Step-by-Step Guide for ParentsStep 1: Continuing Number Sequences and Finding Missing Numbers. At this stage, your child may investigate number patterns and sequences during maths lessons. They may be encouraged to extend a number sequence following a given rule or find missing numbers in a pattern according to a rule.
This page titled 13.3E: Geometric Sequences (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
We provide step by step help with Math homework assignments from 4th grade McGraw Hill textbooks to improve their grades and get an inddepth understanding of the lesson. ... Lesson 3: Hands On: Use the Distributive Property to Multiply ... Lesson 3: Sequences Free Sample Complete Paid Version. Lesson 4: Problem Solving: Look for a Pattern ...
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students construct exponential functions to solve multi-step problems. In the homework, they do the same with linear functions. The lesson addresses focus standard F-BF.A.2, which asks students to write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two ...
Write a formula for Akelia's sequence. Answer: A (n) = 5 + 3 (n - 1) c. Explain how each part of the formula relates to the sequence. Answer: To find each term in the sequence, you are adding 3 one less time than the term number. To get the 1st term, you add three zero times. To get the 2nd term, you add 3 one time.