Quiz about Unit 12 Review - Sequences and Series

Question 1

Which sequence is arithmetic?

Accepted Answer

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

Answer

4, 8, 16, 32, 64, ...

Answer

4, 6, 10, 12, 16, ...

Answer

4, 2, 1, 1/2, 1/4, ...

Question 2

Find the missing terms of the arithmetic sequence:
145, ___, ___, ___, 205

Accepted Answer

160, 175, 190

Answer

165, 185, 195

Answer

155, 165, 175

Answer

190, 175, 160

Question 3

Find S_n for the given series:
a₁=22
d=-8
n=21

Accepted Answer

-1218

Answer

1911

Answer

-1449

Answer

-2436

Question 4

What is the sum of the first 10 terms for the following geometric series:
2 - 6 + 18 - 54 + ...

Accepted Answer

-29524

Answer

59048

Answer

524288

Answer

3069

Question 5

Find the sum for the following series.

Accepted Answer

-682

Answer

44

Answer

-162

Answer

324

Question 6

Which recursive formula best describes the following sequence:
3, 8, 13, 18, 23...

Accepted Answer

a_n = a_n-1+5 ; a₁=3

Answer

a_n = (3)^n-1 ; a₁=5

Answer

a_n = (5)^n-1 ; a₁=3

Answer

a_n = a_n-1+3 ; a₁=5

Question 7

Find the first term of the given sequence:
a₁₄=68
d=3

Accepted Answer

29

Answer

14

Answer

20

Answer

26

Question 8

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

Accepted Answer

-16, -11, -6, -1

Answer

-16, -21, -26, -31

Answer

5, -11, -27, -43

Answer

-16, -80, -500, -200

Question 9

An arithmetic sequence is given below.

16, 13, 10, 7, ...

Which is the explicit formula for the n^th term a_n?

Accepted Answer

a_n= -3n+19

Answer

a_n= -5n+13

Answer

an = 3n+13

Answer

a_n= -5n+20

Question 10

When the lemon tree near my house was first planted (year 0), it measured 16 inches tall. Each year after that, the height seemed to match an arithmetic sequence, by growing 3 inches per year.
How many inches would we expect it to be when n= 40 years from when it was planted?

Accepted Answer

133 inches

Answer

145 inches

Answer

142 inches

Answer

139 inches

Question 11

What is the sum of the series $$2 + 6 + 18 + 54 + ...$$ up to the 6th term?

Accepted Answer

732

Answer

728

Answer

730

Answer

734

Question 12

Find the sum of the geometric series.

Accepted Answer

248

Answer

124

Answer

120

Answer

240

Question 13

What is the sum of the first 8 terms of the geometric series $$3 + 9 + 27 + 81 + ...$$ ?

Accepted Answer

9840

Answer

9841

Answer

3280

Answer

3281

Question 14

Which formula represents the nth term of the sequence 4, 9, 14, 19, ...?

Accepted Answer

5n - 1

Answer

n + 4

Answer

5n + 4

Answer

5n - 5

Question 15

Amy ran 3 miles to prepare for her marathon on the first day of practice. Each day she ran 2 more miles than the previous day. She wrote a formula to see how many miles she would run over the next few days of practice. The formula is shown: $$a_1=3,\ a_n=a_{\left(n-1\right)}+2$$

Which formula is equivalent to the one Amy wrote?

Accepted Answer

$$a_n=1+2n$$

Answer

$$a_n=3n+2$$

Answer

$$a_n=5+2n$$

Answer

$$a_n=7+2n$$

Question 16

Greg posted a tiktok video that received 400 hits the first day. Each day the number of hits doubled. He wrote a formula to see how many hits his video would receive in the next few days. The formula is shown below.

$$a_n=400\left(2\right)^{\left(n-1\right)}$$

Which formula is equivalent to the one Greg wrote?

Accepted Answer

$$a_1=400\ ;\ a_n=2a_{\left(n-1\right)}$$

Answer

$$a_1=2\ ;\ a_n=400a_{\left(n-1\right)}$$

Answer

$$a_1=2\ ;\ a_n=400+a_{\left(n-1\right)}$$

Answer

$$a_1=400\ ;\ a_n=2+a_{\left(n-1\right)}$$

Question 17

What is the rule for the nth term of the sequence given below?

$$14,\ 6,\ -2,\ -10,\ .\ .\ .\ $$

Accepted Answer

$$a_n=22-8n$$

Answer

$$a_n=21-8n$$

Answer

$$a_n=20-9n$$

Answer

$$a_n=22-9n$$

Question 18

Harley wants to calculate the sum of the first six terms of the geometric sequence $$-2,\ -6,\ -18,\ -54,\ .\ .\ .\ $$ Which of the following formulas will she need to use?

Accepted Answer

$$\frac{-2\left(1-\left(3\right)^6\right)}{1-3}$$

Answer

$$\frac{-2\left(1-\left(3\right)^5\right)}{1-3}$$

Answer

$$\frac{-2\left(1-\left(-3\right)^6\right)}{1-\left(-3\right)}$$

Answer

$$\frac{-2\left(1-\left(\frac{1}{3}\right)^6\right)}{1-\frac{1}{3}}$$

Question 19

You and your friend are going to a private concert. The first row in the venue seats 8. Each row after has 3 more in it then the row before. If there are 10 rows in this venue, how many seats are in the venue?

Accepted Answer

$$215$$

Answer

$$210$$

Answer

$$197$$

Answer

$$201$$

Question 20

Maribell wrote an arithmetic sequence where $$a_1=24$$ and the common difference is $$4$$ .

What is a rule for the nth term of this sequence?

Accepted Answer

$$a_n=20+4n$$

Answer

$$a_n=24+6n$$

Answer

$$a_n=18+6n$$

Answer

$$a_n=19+5n$$

Question 21

Find the common ratio: 4, -16, 64, -256, ...

Accepted Answer

r = -4

Answer

r = 2

Answer

r = -2

Answer

r = 4

Question 22

Write the explicit formula for the geometric sequence.

Accepted Answer

a_n = 10(2)^n-1

Answer

a_n = 2(10)^n-1

Answer

a_n = 10(2)ⁿ

Answer

a_n = 2(10)ⁿ

Question 23

Write the explicit formula for the geometric sequence.

Accepted Answer

a_n = 3(-4)^n-1

Answer

a_n = 4(3)^n-1

Answer

a_n = 3(4)^n-1

Answer

a_n = -4(3)^n-1

Question 24

Determine if the following sequence is arithmetic or geometric.

4, 9, 14, 19, 24, ...

Accepted Answer

Arithmetic

Answer

Geometric

Question 25

Determine if the following sequence is arithmetic or geometric.

7, 28, 112, 448, 1792, ...

Accepted Answer

Geometric

Answer

Arithmetic

Question 26

Identify the common ratio for the given geometric sequence.

48, 12, 3, 0.75, ...

Accepted Answer

r = $$\frac{1}{4}$$

Answer

r = 4

Answer

r = -36

Answer

r = 3

Question 27

Identify the common difference of the given arithmetic sequence.

5, 1, -3, -7, ...

Accepted Answer

d = -4

Answer

d = -5

Answer

d = 5

Answer

d = 7

Question 28

Which of the following recursive formulas represents the given sequence.

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 29

Which of the following recursive formulas represents the given sequence.

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

Accepted Answer

$$a_1=7$$ , $$a_n=a_{\left(n-1\right)}\cdot2$$

Answer

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

Answer

$$a_1=7$$ , $$a_n=a_{\left(n-1\right)}\cdot7$$

Answer

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

Unit 12 Review - Sequences and Series

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