Applications of Sequences and Series Learning Objective: to apply sequences and series to real world situations Warm-up (IN) HW/INB Check! When you’re.

Slides:

Advertisements

Similar presentations

3.1 The inverse sine, cosine, and tangent functions Warm-up (IN) 1.What is the domain and range of ? 2.True or False: The graph of is decreasing on the.

Advertisements

2.8 Cont. Warm-up (IN) 1. Graph Learning Objective: To fit a sinusoidal curve to a set of data.

3.8 Trig Equations (cont.) Warm-up (IN) 1.Solve: Learning Objective: to continue to learn techniques that are useful in solving trig identities, including.

7-4A Similar Figures and Proportions Learning Objective: To determine whether two given figures are similar, and to use similarity to find missing lengths.

AAT-A Date: 11/14/13 SWBAT divide polynomials. Do Now: ACT Prep Problems HW Requests: Math 11 Worksheet Start Vocab sheet In class: Worksheets to look.

Curve Fitting Learning Objective: to fit data to non-linear functions and make predictions Warm-up (IN) 1.Find all the critical points for 2.Solve by factoring.

12-3 Infinite Sequences and Series. Hints to solve limits: 1)Rewrite fraction as sum of multiple fractions Hint: anytime you have a number on top,

5.8 Quadratic Inequalities

2.5 Properties of the Trig Functions

4.3 The Inverse of a Matrix Warm-up (IN)

More Practice with Exponential Functions Warm-up Quick Quiz! Learning Objective: to use exponential functions in other real life situations and begin to.

Rational Functions Learning Objective: to find the domain and intercepts for rational functions Warm-up (IN) 1.Factor completely 2.Find the vertex, x-

Consecutive Numbers Algebra I.

1.4 Infinite Geometric Series Learning Objective: to explore what happens when a geometric series is infinite and to express it using sigma notation. Warm-up.

Approximating Zeroes Learning Objective: to be able to find all critical points of a polynomial function. Warm-up (IN) Describe the graph: 1. 2.

1.1 Arithmetic Sequences and Series Warm-up (IN) 1.A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third.

Unit 7: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.

12-1 Arithmetic Sequences and Series. Sequence- A function whose domain is a set of natural numbers Arithmetic sequences: a sequences in which the terms.

3.3 Trig Identities Warm-up (IN) 1.True or False: 2.True or False: Learning Objective: To understand that establishing trig identities provides the skills.

EXAMPLE 5 Find the sum of a series Find the sum of the series. (3 + k 2 ) = ( ) 1 ( ) + ( ) + ( ) + ( ) 8 k – 4 = 19.

2.2 Function Library Learning Objective: to identify different types of functions and their transformations. Also, to graph piecewise functions. Warm-up.

Solving Exponential Equations

1.5 Cont. Warm-up (IN) Learning Objective: to create a scatter plot and use the calculator to find the line of best fit and make predictions. (same as.

Warm-Up Factor. x2 – 10x x2 – 16x + 1 Multiply.

1.6 Continuity CALCULUS 9/17/14. Warm-up Warm-up (1.6 Continuity-day 2)

6-1B Solving Linear Systems by Graphing Warm-up (IN) Learning Objective: to solve a system of 2 linear equations graphically Given the equations: 1.Which.

5.5 Quadratic Formula Warm-up (IN) Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find.

2.6 Special Functions Warm-up (IN) Learning Objective: to write and graph piecewise and absolute value functions and to apply them to real world situations.

13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…

1.1 Cont. Give the first 4 terms of the sequence: a. b. Warm-up (IN)

Rational Functions Learning Objective: To find vertical asymptotes, horizontal asymptotes, holes, and one or two key points, then graph rational functions.

Exponential Functions Learning Objective: to explore the graphs of exponential functions and the natural base. Warm-up (IN) 1.Complete the table. 2.Do.

9.1 Sequences and Series. A sequence is a collection of numbers that are ordered. Ex. 1, 3, 5, 7, …. Finding the terms of a sequence. Find the first 4.

3.4 Sum and Difference Formula Warm-up (IN) 1.Find the distance between the points (2,-3) and (5,1). 2.If and is in quad. II, then 3.a. b. Learning Objective:

Math Agenda 5/11/15 Warm-Up: Mountain Math - # 1 Facing Math HW: None.

3.7 Trig Equations Warm-up (IN) 1.Solve: 2.Find the exact value of: Learning Objective: to identify numerous solutions to trig equations, understand the.

Venn Diagrams Warm-up 1.Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in both classes, how.

3.2 The Inverses Continued Warm-up (IN) 1.What is the domain and range of ? 2.True or False: The graph of is increasing on the interval and. 3. If and,

10.2 Special Right Triangles Learning Objective: To find relationships among side lengths in and triangles and to find distances in real.

6-2B Solving by Linear Combinations Warm-up (IN) Learning Objective: to solve systems of equations using linear combinations. Solve the systems using substitution.

Evaluating Logs and Antilogs Warm-up Solve: Learning Objective: to evaluate and solve equations with logs of bases other than those we’re used to.

1.2 Geometric Sequences and Series Warm-up (IN) 1.Find the sum of the arithmetic series: a …+460 b. Learning Objective: to understand what.

September 11, 2012 Properties and Integers Warm-up: Order of Operations 1.Simplify (3 – 5) – 4  Challenge: Your objective is to use the digits.

Growth and Decay Warm-up More logs quiz and HW/INB check! Learning Objective: to use logarithms to solve real life situations.

1.8 Absolute Value Equations and Inequalities Warm-up (IN) Learning Objective: to write, solve and graph absolute value in math and in real-life situations.

2.6 Cont. Warm-up (IN) 1.Identify the transformations from to 2.Graph Learning Objective: To be able to identify the amplitude, period, 4 sub- intervals,

5-2B Two-Point Equation of a Line Warm-up (IN) Learning Objective: to determine the equation of a line through 2 given points. Rewrite the equations in.

2.5 Cont. Warm-up (IN) Learning Objective: To know the domain and range of the trig functions, and to use the Even-Odd Properties to find the Exact values.

Warm-Up #2 Multiply these polynomials. 1) (x-5) 2 2) (8x-1) 2 3. (4x- 3y)(3x +4y) Homework: P5 (1,3,5,11,13,17,27,33,41, 45,49,55,59,63,71,73,77) Answers:

5.6 Complex Numbers Learning Objective: To classify and find all roots of a quadratic equation and to perform operations on complex numbers. Warm-up (IN)

5-1B Rate of Change Warm-up (IN) Learning Objective: to understand that slope is the rate of change of one quantity relative to another and to be able.

September 19, 2012 More multi-step equations and consecutive integer problems Warm-up: Do one group’s multi-step review sheet. When you are done, compare.

Sum of Arithmetic Sequences. Definitions Sequence Series.

3.6 Product-to-Sum and Sum-to- Product Formulas Warm-up (IN) 1.Find the exact value of: Learning Objective: To be able to properly identify which product-to-sum.

2.8 Phase Shift and Sinusoidal Curve Fitting Warm-up (IN) - none Learning Objective: To graph sinusoidal functions of the form using the amplitude, period,

11.2 Arithmetic Series. What is a series?  When the terms of a sequence are added, the indicated sum of the terms is called a series.  Example  Sequence.

1.2 Cont. Learning Objective: to continue to find terms of sequences and then to find the sum of a geometric series. Warm-up (IN) 1.Give the first 4 terms.

Unit 9: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

Factoring to solve a quadratic TURN IN YOUR WORKSHEET FROM TUESDAY Your chapter 9 quiz is next WED (over )

Warmups Find three consecutive integers whose sum is 96.

Ch. 8 – Sequences, Series, and Probability

3-3 rules for differentiation

Consecutive Numbers Algebra I.

13.3 – Arithmetic and Geometric Series and Their Sums

Adding and subtracting decimals

6.5 Applications of Common Logarithms

Arithmetic Sequences and Series

60 MINUTES REMAINING.

Geometric Sequence Skill 38.

Presentation transcript:

Applications of Sequences and Series Learning Objective: to apply sequences and series to real world situations Warm-up (IN) HW/INB Check! When you’re finished…grab a quiz!

Notes! Ex 1 – find the sum of the positive even integers to …+100 Arith! Ex 2 – how many multiples of 4 are there between 25 and 75? 28, 32, 36,,…, 72 Arith! We need to find n

Ex 3 – a pump removes 5% of the water in a pool each minute. What % remains after 10 minutes? How much is in the pool initially? 100% How much is in the pool the next minute? 95% Then 95% of that, etc. How much is in the pool after 10 minutes?

Ex 4 – John rented an apt in 2003 for $600 a month. If his monthly rent was increased 5% at the end of each year, how much was his monthly rent in 2009?

Ex 5 – a stack of cans has 12 cans on the top layer, 13 on the 2 nd layer, and so on. If there are 20 cans on the bottom layer, how many total cans are on the display? …+20 First we need to find n Now, sum!

HW – Applications worksheet #1-7 Out – None! Summary – Sequences and series are useful because… Don’t forget about POW!!