APPC Arith Geo Intro Notice & Wonder

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
• no

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