APPC Arith Geo Intro Notice & Wonder

Presentation

•

Mathematics

•

11th Grade

•

Easy

•

CCSS

HSF.BF.A.2, HSF.LE.A.2, 5.OA.B.3

Standards-aligned

Phara Cherdsuriya

Used 2+ times

FREE Resource

5 Slides • 25 Questions

Arithmetic & Geometric

Sequence

Objective: Introduce arithmetic & geometric sequences and notice relationships to linear and exponential functions

Multiple Choice

What do you notice in the following four patterns? Which one of the following does not belong?

-10, 10, 30, 50, 70, . .

-4, -1, 2, 5, 8, . . .

-2, 4, -8, 16, - 32, . . .

3, 6. 9. 12, 15, . . .

Multiple Choice

Which of the following is an example of an arithmetic sequence?

4, 8, 16, 32, 64

1, 2, 4, 7, 11

15, 13, 11, 9, 7

3, 6, 12, 24, 48

Multiple Choice

Which sequence is NOT an arithmetic sequence?

-7, -13, -19, -25,...

-10, -6, -2, 2,..

6, 8, 10, 12,...

3, 15, 75, 375,...

Multiple Choice

The first three terms of an arithmetic sequence are as follows

13, 19, 25

What are the next two terms of the sequence?

31 and 37

31 and 36

30 and 37

30 and 36

Graphing

Plot the ordered pairs from the arithmetic sequence 2, 5, 8, on a coordinate plane as (1, 2), (2, 5), (3, 8).
What do you notice about arithmetic sequence?

Multiple Choice

Find the common difference for this arithmetic sequence.
3, 10, 17, 24, ...

d = -6

d = 6

d = 7

d = -7

Multiple Choice

Identify the common difference.
97, 86, 75, 64, ...

d = 8

d = 11

d = -11

d = -8

Multiple Choice

Identify the common difference.
3, 7, 11, 15, ...

d = 6

d = 5

d = 4

d = 2

Multiple Choice

Each individual number in a sequence of numbers is called what?

Common difference

Successive term

Term

Geometric term

Multiple Choice

Which table of values represents a linear function?

Multiple Choice

True or false: Any arithmetic sequence can be written as a linear function, y = mx + b

True

False

I don't know

I don't care at this point

Multiple Choice

Which equation describes this sequence? 1, 3, 5, 7, 9. . .

y = 2(3)^x

y = 2x - 1

y = 2x + 1

y = - 2x + 1

y = -2x - 1

Multiple Choice

Two students are solving the same problem: "Find the 100th term of the arithmetic sequence 1, 4, 7, 10, ..." One student uses the explicit formula an = a1+(n−1)d where an is nth term, a1 is first term, and d is common difference, and the other uses the linear function f(x)=3x−2. Critique both approaches. Which is more efficient, and why? When might you prefer one method over the other?

Both methods are correct and equally efficient for finding the 100th term; use whichever you remember.

Both methods are correct, but Student B's linear function is more efficient here because evaluating f(100) is simpler than substituting into an = a1 +(n−1)d.

Both methods are correct, but Student A's explicit formula an=a1+(n−1)d is more direct and clearer for sequences—so it is slightly preferable; however, the linear function is handy if you want to interpret the sequence as a function of position.

Student A is correct and Student B is incorrect because a sequence must use the sequence formula, not a function; only Student A's answer is valid.

What is Geometric Sequence?

Multiplying a constant # over and over

Example 1) 20, -40, 80, -160, 320, -640, , . . . .

Example 2) 28000, 14000, 7000, 3500, ...

Example 3) Fractals! (Real-life example)

Multiple Choice

Find the common ratio for the geometric sequence: -192, 48, -12, 3, . . .

r = -4

r = 4

r = 1/4

r = -1/4

Multiple Choice

Find the common ratio for the geometric sequence.

r = 10

r = 1/2

r = 2

r = 4

Multiple Choice

Is the sequence-4, -12, -36, -108,... geometric?

yes

Multiple Choice

Is the sequence 9, 99, 999, 9999,... geometric? Why?

no, 99/9, 999/99, 9999/999 are not constant and therefore, it is not multiplying by same # pattern which indicates geometric sequence

yes, it a same # multiplying pattern

Multiple Choice

What is the equation of the following table?

HINT: Use your STAT Key on your calculator

y = 7(2)^x

y = 4x + 7

Multiple Choice

What is the equation of the following table?

HINT: Use your STAT Key on your calculator

y = 2x + 4

y = 4(2)^x

Multiple Choice

Which table represents the following equation?

Multiple Choice

True or false: Geometric sequence can be written as exponential function since it is multiplying by a constant

True

False

I don't know

AP Precalculus is too difficult! I don't care at this point : (

Multiple Choice

Which equation best describes this sequence? 800, - 400, 200, - 100...

y = 800(-2)^x

y = 800(2)^x

y = - 800(0.5)^x

y = 800(-0.5)^x-1

y = 800 - 2x

Multiple Choice

Is the table linear, exponential, or quadratic?

Linear

Exponential

Quadratic

none of these

Multiple Choice

This table represents what kind of function?

Linear

Exponential Growth

Exponential Decay

Quadratic

Multiple Choice

Identify the type of relationship

Linear

Quadratic

Exponential

Arithmetic & Geometric

Sequence

Objective: Introduce arithmetic & geometric sequences and notice relationships to linear and exponential functions

Show answer

Auto Play

Slide 1 / 30

SLIDE

Similar Resources on Wayground

23 questions

Triangle Inequality Theorem

Presentation

•

11th Grade

20 questions

Mixed Numbers

Presentation

•

4th - 5th Grade

24 questions

1/19 Key Features of Polynomial Graphs

Presentation

•

11th Grade

19 questions

Inverse Functions

Presentation

•

11th Grade

23 questions

Simulador 4to Parcial M2: Razones Trigonométricas

Presentation

•

11th Grade

21 questions

Similar Triangles

Presentation

•

10th Grade

24 questions

Computer Networks

Presentation

•

11th Grade

23 questions

9.6 Vectors in Space

Presentation

•

10th - 12th Grade

Popular Resources on Wayground

24 questions

PBIS-HGMS Day 10

Quiz

•

6th - 8th Grade

10 questions

HCS SCI 03 Summer School Review 3

Quiz

•

3rd Grade

11 questions

Home Scope

Quiz

•

7th - 8th Grade

15 questions

HCS SCI 05 Summer School Assessment 3 Review

Quiz

•

5th Grade

35 questions

Lufkin Road Middle School Student Handbook & Policies Assessment

Quiz

•

7th Grade

18 questions

Geo 11.3 Area of Circles and Sectors

Quiz

•

9th - 11th Grade

Discover more resources for Mathematics

18 questions

Geo 11.3 Area of Circles and Sectors

Quiz

•

9th - 11th Grade