5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.

Slides:



Advertisements
Similar presentations
Geometric Sequences.
Advertisements

5-Minute Check on Chapter 2
Geometric Sequences and Series
Lesson 14-1 Counting Outcomes. 5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
4.7 Arithmetic Sequences A sequence is a set of numbers in a specific order. The numbers in the sequence are called terms. If the difference between successive.
2-3 Geometric Sequences Definitions & Equations
11.3 – Geometric Sequences.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
5-Minute Check on Chapter 2
Transparency 7 Click the mouse button or press the Space Bar to display the answers.
Lesson 4-7 Arithmetic Sequences.
Geometric Sequences and Series
Lesson 1-3 Distance and Midpoint.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
Lesson 3-7 Percent of Change.
5-Minute Check on Chapter 2
5-Minute Check on Lesson 7-2 Transparency 7-3 Click the mouse button or press the Space Bar to display the answers. Find x Determine whether.
Lesson 8-1 Multiplying Monomials. Transparency 1 Click the mouse button or press the Space Bar to display the answers.
Lesson 8-2 Dividing Monomials. Transparency 2 Click the mouse button or press the Space Bar to display the answers.
What are two types of Sequences?
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
Geometric Sequences as Exponential Functions
Lesson 12-1 Inverse Variation. Objectives Graph inverse variations Solve problems involving inverse variations.
5-Minute Check on Lesson 7-1 Transparency 7-2 Click the mouse button or press the Space Bar to display the answers. Find the geometric mean between each.
Lesson 3-8 Solving Equations and Formulas. Objectives Solve equations for given variables Use formulas to solve real-world problems.
5-Minute Check on Lesson 11-4 Transparency 11-5 Click the mouse button or press the Space Bar to display the answers. Find the area of each figure. Round.
Elimination Using Multiplication
Lesson 10-7 Geometric Sequences.
Multiplying Polynomials
Transparency 3 Click the mouse button or press the Space Bar to display the answers.
Solving Multi-Step Inequalities
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
Arithmetic and Geometric Sequences Finding the nth Term 2,4,6,8,10,…
Statistics: Scatter Plots and Lines of Fit
Solving Open Sentences Involving Absolute Value
Lesson 11-1 Simplifying Radical Expressions. 5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the.
Algebra 2B Chapter 9. Lesson 9.1 Learning Targets: I can simplify Rational Expressions I can simplify complex fractions.
Lesson 5-5 Writing Equations in Point-Slope Form.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
Lesson 6-6 Graphing Inequalities in Two Variables.
Lesson 5-2 Slope and Direct Variation. Transparency 2 Click the mouse button or press the Space Bar to display the answers.
Lesson 3-1 Writing Equations. 5-Minute Check on Chapter 2 Transparency Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
Transparency 2 Click the mouse button or press the Space Bar to display the answers.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
6.8A-Geometric Sequence Objective – TSW use geometric sequences.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
May 1, 2012 Arithmetic and Geometric Sequences Warm-up: What is the difference between an arithmetic and geometric sequence? Write an example for each.
+ 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 7-7 Law of Cosines. 5-Minute Check on Lesson 7-6 Transparency 7-7 Click the mouse button or press the Space Bar to display the answers. Find each.
5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find.
5-Minute Check on Chapter 2
Ratios and Proportions
Lesson 8-8 Special Products.
Click the mouse button or press the Space Bar to display the answers.
Click the mouse button or press the Space Bar to display the answers.
11.3 – Geometric Sequences.
5-Minute Check on Chapter 2
Chapter 6.3 Solving Quadratic Functions by Factoring Standard & Honors
5-Minute Check on Chapter 2
5-Minute Check on Chapter 2
11.3 – Geometric Sequences.
Sequence: A list of numbers in a particular order
5-Minute Check on Chapter 2
Splash Screen.
Presentation transcript:

5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) 5.A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Which of the following is a true statement Standardized Test Practice: ACBD 8/4 < 4/8-4/8 < -8/4-4/8 > -8/4-4/8 > 4/8

Lesson 10-7 Geometric Sequences

Transparency 7 Click the mouse button or press the Space Bar to display the answers.

Transparency 7a

Objectives Recognize and extend geometric sequences Find geometric means

Vocabulary Geometric sequence – Common ratio – Geometric means –

Four Step Problem Solving Plan Step 1: Explore the Problem –Identify what information is given (the facts) –Identify what you are asked to find (the question) Step 2: Plan the Solution –Find an equation the represents the problem –Let a variable represent what you are looking for Step 3: Solve the Problem –Plug into your equation and solve for the variable Step 4: Examine the Solution –Does your answer make sense? –Does it fit the facts in the problem?

Example 1a Determine the pattern A. Determine whether the sequence is geometric. 1, 4, 16, 64, 256, … In this sequence, each term in found by multiplying the previous term by 4. Answer: This sequence is geometric.

Example 1b B. Determine whether the sequence is geometric. 1, 3, 5, 7, 9, 11, … Determine the pattern In this sequence, each term is found by adding 2 to the previous term. Answer: This sequence is arithmetic, not geometric.

Example 2a The common factor is –1.4. Use this information to find the next three terms. 20, –28, 39.2 Find the next three terms in the geometric sequence. 20, –28, 39.2, … Divide the second term by the first. – – Answer:The next 3 terms are –54.88, , and –

Example 2b Divide the second term by the first Answer:The next three terms are 27, 20.25, and Find the next three terms in the geometric sequence. 64, 48, 36, … The common factor is 0.8. Use this information to find the next three terms. 64, 48, 36

Example 3 Geography The population of the African country of Liberia was about 2,900,000 in If the population grows at a rate of about 5% per year, what will the population be in the years 2003, 2004, and 2005? The population is a geometric sequence. The first term is 2,900,000 and the common ratio is Answer:The population of Liberia in the years 2003, 2004, and 2005 will be about 3,524,968, 3,701,217, and 3,886,277, respectively. YearPopulation ,900, ,900,000(1.05) or 3,045, ,045,000(1.05) or 3,197, ,197,250(1.05) or 3,357, ,357,112.5(1.05) or 3,524, ,524,968.1(1.05) or 3,701, ,701,216.5(1.05) or 3,886,277.3

Example 4 Find the eighth term of a geometric sequence in which Formula for the nth term of a geometric sequence Answer:The eighth term in the sequence is 15,309.

Example 5 Find the geometric mean in the sequence 7, ___, 112. In the sequence, and To find you must first find r. Formula: nth term of a geometric sequence Divide each side by 7. Simplify. Take the square root of each side. If r = 4, the geometric mean is 7(4) or 28. If r = -4, the geometric mean is 7(–4) or –28. Answer:The geometric mean is 28 or –28.

Example 5, alternate way Find the geometric mean in the sequence 7, ___, 112. The geometric mean (GM) of two numbers, a and b, is the square root of their product: GM =  a  b. The geometric mean in the sequence, 7, ___, 112 would be (the number between them) GM =  7  112 =  784 =  28. Check: (using r from last page) 7  4 = 28 and 28  4 = 112

Summary & Homework Summary: –A geometric sequence is a sequence in which each term after the nonzero first term is found by multiplying the previous term by a constant called the common ratio r, where r ≠ 0 or 1 –The nth term an of a geometric sequence with the first term a 1 and a common ratio r is given by a n = a 1 r n-1 Homework: –none