12.1-12.3 Test Review (Sequences)

12.1-12.3 Test Review

by Stephanie Kellogg

Multiple Choice

To find the next term in an arithmetic sequence…

• add the common difference d

• multiply by the common ratio r

Multiple Choice

Which of the following is not an arithmetic sequence?

• 1/2, 1, 3/2, 2

• 11, 14, 17, 20

• 2, 4, 8, 16

• 5, 2, -1, -4

Multiple Choice

Identify the common difference in the sequence shown below:

-9, -13, -17, -21,...

• 4

• -4

Multiple Choice

Identify the common difference of the sequence below:

-2.3, -1.1, 0.1, 1.3,...

• -1.2

• 1.3

• 1.2

• -1.3

Multiple Choice

Identify the next three terms of the sequence below:

-6, -10, -14,...

• -17, -21, -25

• 17, 21, 25

• 18, 22, 26

• -18, -22, -26

Multiple Choice

What is the 20^th term of the arithmetic sequence shown below.

7, 4, 1,...

• -49

• 50

• -50

• -51

Multiple Choice

To find the next term in a geometric sequence…

• add the common difference d

• multiply by the common ratio r

Multiple Choice

2, 10, 50, 250, 1250, ...

Is this sequence arithmetic, geometric, or neither?

• arithmetic (common difference d = 5)

• geometric (common ratio r = 5)

• neither (no common difference OR common ratio)

Multiple Choice

400, 100, 25, ...

Is this sequence arithmetic, geometric, or neither?

• arithmetic (common difference d = 6)

• geometric (common ratio r = 1/4)

• neither (no common difference OR common ratio)

Multiple Choice

A sequence can be generated by using a_n = 5a_n-1

where a₁ = 3.

What is the first term in the sequence?

• 3

• 5

Multiple Choice

A sequence can be generated by using a_n = 5a_n-1

where a₁ = 3.

What is the common ratio (r) in the sequence?

• 5

• 3

• neither of these

Multiple Choice

A sequence can be generated by using a_n = a_n-1 +9

where a₁ = 4.

What is the first term in the sequence?

• 9

• 4

Multiple Choice

A sequence can be generated by using a_n = a_n-1 +9

where a₁ = 4.

What is the common difference (d) in the sequence?

• 9

• 4

Multiple Choice

Is the sequence geometric? If so, identify the common ratio.

6, 12, 24, 48

• yes, r=2

• yes, r=-2

• yes, r=4

• no

Multiple Choice

What is the difference between an arithmetic sequence and a geometric sequence?

• One is the sum of the numbers and one is just a list of numbers.

• One has a common difference and one has a common ratio.

• One you can write an nth term and one you cannot.

• None of these are correct.

Multiple Choice

Create the explicit formula for the arithmetic sequence:

2, 8, 14, ...

(Hint:  Write your formula and then simplify it.)

• a_n=2+6n

• a_n=-6+6n

• a_n=6n-4

• a_n=4-6n

Multiple Choice

Given the sequence:  25, 21, 17, 13,...

Write the explicit formula for the arithmetic sequence.  

(Hint:  Simplify your equation.)

• a_n = 4n + 29

• a_n = -4n + 25

• a_n = -4n + 29

• a_n = 4n + 25

Multiple Choice

Which of the following recursive formulas represents the given sequence.

4, 12, 20, 28, 36, ...

• $$a_1=4$$ , $$a_n=a_{\left(n-1\right)}\cdot3$$

• $$a_1=4$$ , $$a_n=a_{\left(n-1\right)}+8$$

• $$a_1=4$$ , $$a_n=a_{\left(n-1\right)}-8$$

• undefined , $$a_n=a_{\left(n-1\right)}\cdot9$$

Multiple Choice

Which of the following recursive formulas represents the given sequence.

7, 14, 28, 56, 112, ...

• $$a_1=7$$ , $$a_n=a_{\left(n-1\right)}+7$$

• $$a_1=7$$ , $$a_n=7\cdot a_{\left(n-1\right)}$$

• $$a_1=7$$ , $$a_n=2\cdot a_{\left(n-1\right)}$$

• $$a_1=7$$ , $$a_n=a_{\left(n-1\right)}+14$$

Multiple Choice

Write the explicit formula for the sequence.

216, 72, 24, 8, ...

• $$a_n=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$$

• $$a_n=8\cdot3^{\left(n-1\right)}$$

• $$a_n=216-144\left(n-1\right)$$

• $$a_n=216\cdot3^{\left(n-1\right)}$$

Multiple Choice

Find a₆.

1, 3, 9, 27, 81, ...

• 243

• 81

• 729

• 3

Multiple Choice

Find a₇.

15, 20, 25, 30, 35, ...

• 25

• 35

• 40

• 45

Poll

Which describes your understanding of arithmetic and geometric sequences?

• I'm an EXPERT!

• I'm GETTING THERE!

• I need MORE PRACTICE!

• HELP! HELP!