Lesson 2 geometric sequences answers

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# Lesson 2 geometric sequences answers

The warm-up asks students to calculate the quantities that have increased or decreased by a certain percent. Students benefit from reviewing how to express a growth factor as the rate of increase added to one and a decay factor as the rate of decrease subtracted from one. Understanding this method of calculating percent increase and decrease is essential for solving applied problems with geometric sequences and series formulas.

While students work, I display homework answers on the overhead and circulate around the room to assign a score to each student's work according to my homework rubric. As I do this, I note what parts of the assignment were difficult and make sure we review those as a group.

I ask for volunteers to put some problems on the board or show students the solution myself if one part of the assignment was difficult for many students. After the homework discussion, I ask students to pair up to compare answers to the warm-up.

I ask about strategy and highlight the efficiency of multiplying by 1 plus the rate when calculating a percent increase and 1 minus the rate when calculating a percent decrease. I send students a quick poll with one additional tip calculation problem after this discussion and ask students to respond with the one step expression for calculating the tip NOT the final answer.

This lesson parallels that of the previous day.

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Here, we focus our attention on geometric patterns and learn the formal methods of defining geometric number patterns explicitly and recursively.

In this lesson, we focus on the geometric sequences from this activity. Using the sequence strips labeled bgh and jI ask students to work together to come up with a rule that expresses the term in terms of n, the term's position in the sequence [MP7]. As students work together, I offer support and hints as necessary. When students have had time to develop these rules, I ask them to share their ideas using a quick poll on the TI NSpire Navigator System.

When we have a collection to look at, we check each idea together to see if substituting 1 for n yields the correct initial term, 2 for n yields the correct second term, etc. This leads to a discussion of sequence notation and how it is similar to and different from exponential function notation.

After the group discussion of student findings, I write the formulas on the board and we work a few examples of using the formulas to find the nth term, the term number, or the common ratio. We also examine the graph of a geometric sequence and compare it to the graph of an exponential function.

Students take note of the formulas, illustrations and examples that I write on the board and actively participants in the discussion.Recommend Documents. Practice file answer key. Practice Test Answer Key. Chapter 1 Introduction to Geometry. Problem Set A. N largerlr? Unit 1. Working with words. Exercise 1. Exercise 2. Advanced Reading Practice 2 answer key.

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Answer Key. Answer Key Pearson Longman TEST 3A. TEST 3B. In the new plant, water from the river would pass through a turbine in the. Answer Key All dolphin vocalizations are emitted from the animal's mouth. Color Patterns. A dolphinLine list or line listing. A line listing is a table in which each row typically represents one person or case of disease, and each column represents a variable such as ID, age, sex, etc.

Nominal variables are qualitative or categorical variables. Age and lymphocyte count are ratio variables because they are both numeric variable with true zero points. Ratio variables are continuous and quantitative variables. Because the centers of each distribution line up, they have the same measure of central location. But because each distribution is spread differently, they have different measures of spread. B, C, E. A skewed distribution is not symmetrical.

For a distribution such as that shown in Figure 2. The median is the value that has half the observations below it and half above it. The mean is the value that is statistically closest to all of the values in the distribution. The geometric mean is the value that is statistically closest to all of the values in the distribution on a log scale. The mode is the value that occurs most often. A distribution can have one mode, more than one mode, or no mode.

In this distribution, both For a distribution with an even number of values, the median falls between 2 observations, in this situation between the 7 th and 8 th values. The 7 th value is The mean is the average of all the values. Given 14 temperatures that sum to The midrange is halfway between the smallest and largest values.

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Since the lowest and highest temperatures are This is the first Notice and Wonder activity in the course. Students are shown four sequences. What do you wonder? After students have had a chance to write down their responses, ask several students to share things they noticed and things they wondered. Record these for all to see. The purpose is to make a mathematical task accessible to all students with these two approachable questions. By thinking about them and responding, students gain entry into the context and might get their curiosity piqued.

Students likely encountered it in an earlier course when they studied exponential functions.

Students notice and describe that each sequence is characterized by the same type of relationship between consecutive terms. When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see MP6.

They might first propose less formal or precise language, and then restate their observation with more precise language in order to communicate more clearly. The last two sequences may present a challenge since the growth factor is less than 1. The purpose of including these sequences is to encourage students to notice and make use of structure MP7.

If they notice that in the first two sequences, each pair of consecutive terms has the same quotient, they could inspect the quotients in the last sequence. These two sequences also give opportunity to point out that we still use "growth factor" even when the terms are decreasing.

Display the four sequences for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner, followed by a whole-class discussion.

Ask students to share the things they noticed and wondered.

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Record and display their responses for all to see. If possible, record the relevant reasoning on or near the sequence. If the idea of each consecutive term in a sequence growing by the same factor or having a common ratio does not come up during the conversation, ask students to discuss this idea.

Encourage students to use the word term, and to be specific when they describe what is happening, for example. Emphasize that the growth factor is defined to be the multiplier from one term to the next; said another way, the quotient of a term and the previous term.

In earlier courses, students may have learned that a ratio has two or more parts. In more advanced courses like this oneratio is sometimes used as a synonym for quotient. In this activity, students generate two geometric sequences from a mathematical situation.

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The purpose is to create representations of geometric sequences using tables and graphs. At this time, students do not need to write equations for the situation since that work will be the focus of a future lesson. Monitor for students sketching neat and accurate graphs to highlight during the whole-class discussion. Note that future lessons will focus on a reasonable domain for sequences when regarded as functions.

Arrange students in groups of 2.Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? All Categories. Grade Level. Resource Type. Log In Join Us. View Wish List View Cart. Results for geometric sequences foldable Sort by: Relevance.

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### Skills Practice Geometric Sequences Answer Key

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Geometric Sequence Formula

This foldable provides an organized way of taking notes. It easily compares the rules and examples for arithmetic and geometric sequences. Now with 2 options! An answer key is included! Looking for extra practice on this skill? MathAlgebra. PrintablesMath CentersInteractive Notebooks. Add to cart.

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Wish List. Geometric Sequences Foldable. This fun foldable is great to review or introduce the explicit and recursive formulas of a geometric sequence. AlgebraAlgebra 2. Fun StuffGraphic Organizers.Winterbreak Tic-Tac Toe. U5 L1 Notes: Function Notation.

U5 Lesson 3: Domain and Range. U5 Lesson 4: Graphing Stories. U5 Lesson 5: Intro to Sequences. Graphing Stories Practice WS if time.

### Recursive And Explicit Answer Key

Warm-up: Exponents. Notes - Exponent Rules. HW: Finish Exponent Packet. Warm-up: Exponents Review. The Perfect Rectangle. Simplify Radicals Notes.

HW: Simplify Radicals Worksheet. Practice Problems. HW: none. Quick Check. HW: Simplify Radicals Worksheet 2. HW: Arithmetic Sequences Worksheet. HW: Geometric Sequences Worksheet. Geometric Sequemces Notes. Recursive Formulas. HW: Recursive Sequences Worksheet. Extra Practice WS. Sequences Key Facts Chart. HW: Finish extra Practice Sheet if needed. In-class review. Review Worksheet. HW: Sequences Review Worksheet. Formative Assessment - Unit 5. HW: Review Worksheet due tomorrow.

M3 Lesson 11 Notes Investigation. Class Discussion. Lesson 14 - Desmos Activity. Return Tests. HW: Lesson 14 WS. Skittles Lab. Notes - Exponential Decay vs. Exponential Growth.

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Request access. Difficulty level:. A geometric sequence or progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number, called the common ratio.

## Arithmetic And Geometric Sequences Answer Key

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Find the Formula for the General Request access Already have an account? Login here. The smart way to improve grades. Maths Year 8 Algebra: Sequences and Terms. Geometric Sequences. In this worksheet, students find the missing term in geometric sequences. Worksheet Overview.

This means that dividing consecutive terms gives the same number. Example Work out the missing term in this geometric sequence: 7, 14, 28,?