Ch.5 Closure Jeopardy

What kind of sequence?

Arithmetic Sequences

Geometric Sequences

Solving Systems of Equations

100

Consider the sequence:

t(n) = 5, 9, 13, 17, ...

Is this sequence arithmetic, geometric, or neither? Why?

Consider the sequence:

t(n) = 5, 9, 13, 17, ...

This is an arithmetic sequence because it always adds by a constant (the common difference). In this case the common difference is 4.

100

Consider the sequence:

t(n) = 1, 5, 9, 13, 17, ...

A. Find the next three terms.

B. What is the common difference?

C. What is t(0)?

Consider the sequence:

t(n) = 1, 5, 9, 13, 17, ...

A. Find the next three terms: 21, 25, 29

B. What is the common difference? +4

C. What is t(0)? -3

100

Consider the sequence:

t(n) = 10, 20, 40, 80, ...

A. Find the next three terms.

B. What is the common multiplier?

C. What is t(0)?

Consider the sequence:

t(n) = 10, 20, 40, 80, ...

A. Find the next three terms. 160, 320, 640

B. What is the common multiplier? 2

C. What is t(0)? 5

100

Match each system of equations below with the best method to solve that system. Do not solve!

1. 2x + y = 12 2. y = 3x - 8 3. x = 3y-5

-2x + 3y = 8 y = 2x - 4 2y + x = 10

Methods:

Equal values Substitution Elimination

Match each system of equations below with the best method to solve that system. Do not solve!

1. 2x + y = 12 2. y = 3x - 8 3. x = 3y-5

-2x + 3y = 8 y = 2x - 4 2y + x = 10

Elimination Equal Values Substitution

200

Consider the sequence:

t(n) = 4,12,36,108,..

Is this sequence arithmetic, geometric, or neither? Why?

The sequence:

t(n) = 4,12,36,108,..

Is geometric because it has a constant multiplier of 3.

200

Consider the sequence:

t(n) = -15.5, -21, -26.5, -32, ...

A. Find the next three terms.

B. What is the common difference?

C. What is t(0)?

Consider the sequence:

t(n) = -15.5, -21, -26.5, -32, ...

A. Find the next three terms. -37.5, -43, -48.5

B. What is the common difference? -5.5

C. What is t(0)? -10

200

Consider the sequence:

t(n) = 48, 24, 12, 6, 3, ..

A. Find the next three terms.

B. What is the common multiplier (not common divider)?

C. What is t(0)?

Consider the sequence:

t(n) = 48, 24, 12, 6, 3, ..

A. Find the next three terms. 1.5, .75, .375

B. What is the common multiplier (not common divider)? 1/2 = 0.5

C. What is t(0)? 96

200

Solve the following system of equations using substitution:

x = 3y - 4

2x + 3y = 19

x = 3y - 4

2x + 3y = 19 --> 2(3y-4) + 3y = 19

--> 9y - 8 = 19 --> 9y = 27 --> y=3

Solution: (5,3) or x=5, y=3

300

Consider the sequence:

t(n) = 10, 8.7, 7.4, 6.1, ...

Is this sequence arithmetic, geometric, or neither? Why?

The sequence:

t(n) = 10, 8.7, 7.4, 6.1, ...

Is arithmetic because it always adds by a common difference. In this case, the common difference is -1.3.

300

Consider the sequence:

t(n) = 20, 13, 6, -1, ...

What is the explicit equation for this sequence?

Consider the sequence:

t(n) = 20, 13, 6, -1, ...

What is the explicit equation for this sequence?

t(n) = -7n + 27

300

Consider the sequence:

t(n) = 20, 80, 320, ...

What is the explicit equation for this sequence?

Consider the sequence:

t(n) = 20, 80, 320, ...

What is the explicit equation for this sequence?

t(n) = 5(4)ⁿ

300

Solve the following system of equations using elimination:

3x - 4y = 18

5x + 4y = -2

3x - 4y = 18

5x + 4y = -2 ---> 8x = 16 --> x = 2

Solution (2,-3) or x=2, y=-3

400

Consider the sequence:

t(n) = 1215, 405, 135, 45, ...

Is this sequence arithmetic, geometric, or neither? If the sequence is arithmetic, find the common difference (there is no such thing as a common subtracter). If the sequence is geometric, find the common multiplier (there is no such thing as a common divider).

The sequence:

t(n) = 1215, 405, 135, 45, ...

Is geometric. Its common multiplier is 1/3.

400

Consider the sequence:

t(n) = -8, -1, 6, 13, ...

1. What is the explicit equation for this sequence?

2. Use your explicit equation to find t(38).

Consider the sequence:

t(n) = -8, -1, 6, 13, ...

1. What is the explicit equation for this sequence?

t(n) = 7n-15

2. Use your explicit equation to find t(38).

t(38) = 251

400

Consider the geometric sequence:

t(n) = 375, 225, 135, 81, ...

What is the explicit equation for this sequence?

Consider the geometric sequence:

t(n) = 375, 225, 135, 81, ...

What is the explicit equation for this sequence?

t(n) = 625(3/5)ⁿ = 625(.6)ⁿ

400

Solve the following system of equations using substitution:

x = 8 - 3y

5y - 3x = 32

x = 8 - 3y

5y - 3x = 32 --> 5y - 3(8-3y) = 32

--> 5y - (24-9y) = 32

--> 5y - 24 + 9y = 32

--> 14y = 56 --> y = 4

Solution: (-4,4) or x=-4, y=4

500

Consider the sequence:

t(n) = 3, 5, 9, 15, 23, ...

The sequence generator is +2, +4, +6, +8, ...

Millie says this is an arithmetic sequence because it is adding and it is adding in a consistent way. Is she correct or not? Why or why not?

The sequence:

t(n) = 3, 5, 9, 15, 23, ...

Is not arithmetic because it does not add by a constant value.

500

Consider the sequence:

t(n) = 5, 1, -3, -7, ...

1. Find the explicit equation.

2. Use your explicit equation to find n then t(n) = -423

Consider the sequence:

t(n) = 5, 1, -3, -7, ...

1. Find the explicit equation.

t(n) = -4n + 9

2. Use your explicit equation to find n then t(n) = -423

t(108) = -4(108) + 9 = -423, so n=108

500

Consider the geometric sequence:

t(n) = 900, 300, 100, ...

1. What is the explicit equation for this sequence?

2. Use your explicit equation to find t(10)

Consider the geometric sequence:

t(n) = 900, 300, 100, ...

1. What is the explicit equation for this sequence?

t(n) = 2700(1/3)ⁿ

2. Use your explicit equation to find t(10)

t(10) = 2700(1/3)¹⁰ = 0.0457...

500

Solve the following system of equations using elimination:

6x - 5y = 18

15x + 2y = 132

6x - 5y = 18 x5 --> 30x - 25y = 90

15x + 2y = 132 x(^-2) --> -30x - 4y = -264

-29y = -174 --> y=6

Solution: (8,6) or x=8, y=6