Quiz about Arithmetic and Geometric Sequences Review with Explicit Formulas

Question 1

Create the formula for the sequence:
2, 8, 14, ...

Accepted Answer

an=6n-4

Answer

an=2+6n

Answer

an=-6+6n

Answer

an=4-6n

Question 2

Identify the common difference.
10, 20, 30, 40, ...

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 3

Identify the common difference.
-21, -18, -15, -12, ...

Accepted Answer

3

Answer

4

Answer

-4

Answer

-3

Question 4

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

Accepted Answer

-11

Answer

8

Answer

11

Answer

-8

Question 5

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

Accepted Answer

4

Answer

6

Answer

5

Answer

2

Question 6

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

Accepted Answer

127

Answer

32

Answer

64

Answer

356

Question 7

Find the 32nd term of this sequence.
9, 4, -1, -6, -11, ...

Accepted Answer

-146

Answer

81

Answer

-34

Answer

-225

Question 8

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.

Accepted Answer

a_n= -4n + 29

Answer

a_n = 4n + 29

Answer

a_n = -4n + 25

Answer

a_n = 4n + 25

Question 9

What are the next 3 terms in this sequence of terms? 3, 7, 11, 15

Accepted Answer

19, 23, 27

Answer

18, 22, 26

Answer

19, 21, 23

Answer

18, 21, 24

Question 10

What is the distance from one number to the next in a sequence of numbers that is represented by a (d) in an arithmetic sequence?

Accepted Answer

Common difference

Answer

Common denominator

Answer

Common opposites

Answer

Common domain

Question 11

The next two terms of the sequence 4,7,10,13 are

Accepted Answer

16 and 19

Answer

15 and 19

Answer

16 and 18

Answer

15 and 18

Question 12

The next term of the sequence 2,4,8,16 are

Accepted Answer

32

Answer

64

Answer

108

Answer

20

Question 13

The next two terms of the sequence 12,17,22,27 are

Accepted Answer

27 and 32

Answer

28 and 33

Answer

29 and 34

Answer

30 and 35

Question 14

The pattern followed by the sequence 3,6,9,12 is...

Accepted Answer

Multiple of 3

Answer

prime no.s

Answer

odd no.s

Answer

multiple of 6

Question 15

The next term of the series 4,16,64 is

Accepted Answer

256

Answer

132

Answer

120

Answer

150

Question 16

The next term of the series 11,8,5,2 are

Accepted Answer

-1

Answer

-2

Answer

1

Answer

2

Question 17

Is the sequence geometric or arithmetic?
3, 6, 9, 12...

Accepted Answer

Arithmetic

Answer

Geometric

Answer

Neither

Question 18

Is the sequence geometric or arithmetic?
6, 18, 54...

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Neither

Question 19

What is the common ratio for the sequence:
3, 15, 75...

Accepted Answer

5

Answer

12

Answer

1/5

Question 20

What is the explicit rule for the sequence:
11, 22, 44, 88...

Accepted Answer

a_n = 11(2)^n-1

Answer

a_n = 2(11)^n-1

Answer

an = 11x2

Question 21

What is the common difference of this sequence?

Accepted Answer

3

Answer

4

Answer

7

Answer

1

Question 22

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

Accepted Answer

2

Answer

4

Answer

3

Answer

6

Question 23

Find the 22nd term of the following sequence:
5, 8, 11, ...

Accepted Answer

68

Answer

14

Answer

63

Answer

71

Question 24

Which formula is used to find the explicit equation for arithmetic sequences?

Accepted Answer

a_n = a₁ + d(n-1)

Answer

a_n = a_n-1 + d

Answer

a_n = a_n-1 * r

Answer

a_n = a₁ * r^n-1

Question 25

Which formula is used to find the recursive equation for arithmetic sequences?

Accepted Answer

a_n = a_n-1 + d

Answer

a_n = a_n-1 * r

Answer

a_n = a₁ + d(n-1)

Answer

a_n = a₁ * r^n-1

Question 26

Which formula is used to find the explicit equation for geometric sequences?

Accepted Answer

a_n = a₁ * r^n-1

Answer

a_n = a_n-1 + d

Answer

a_n = a_n-1 * r

Answer

a_n = a₁ + d(n-1)

Question 27

Which formula is used to find the recursive equation for geometric sequences?

Accepted Answer

a_n = a_n-1 * r

Answer

a_n = a_n-1 + d

Answer

a_n = a₁ + d(n-1)

Answer

a_n = a₁ * r^n-1

Question 28

What is the explicit formula the following arithmetic sequence?

Accepted Answer

3n

Answer

3(2)n-1

Answer

2(3)n-1

Answer

3 + 3n

Question 29

Find the missing terms in the arithmetic sequence
1, __, __, __, 29,...

Accepted Answer

8, 15, 22

Answer

7, 15, 23

Answer

-8, 15, -22

Answer

3, 9, 27

Question 30

Find the missing terms in the geometric sequence
2, __, __, __, 13122,...

Accepted Answer

18, 162, 1458

Answer

3283, 6562, 9843

Answer

22, 1222, 6022

Answer

16, 128, 1024

Question 31

Given a₁= 8 and r= 1/2 find a₆

Accepted Answer

1/4

Answer

1/8

Answer

1/2

Answer

4

Question 32

Given a₁= 5 and d= 2 find a₆

Accepted Answer

15

Answer

13

Answer

10

Answer

17

Question 33

Find the missing term of the arithmetic sequence.
-15, __, 1, ...

Accepted Answer

-7

Answer

3

Answer

5

Answer

-10

Question 34

Find the missing term of the arithmetic sequence.
..., 98, __, 66, ...

Accepted Answer

82

Answer

85

Answer

84

Answer

83

Question 35

Sweet Time Bakery just opened and is increasing the number of items they bake. For example, the bakery made 150 carrot cakes in January, 133 carrot cakes in February, 116 carrot cakes in March, and 99 carrot cakes in April. What kind of sequence is this?

Accepted Answer

Arithmetic

Answer

Geometric

Answer

Both

Answer

Neither

Question 36

Carey is organizing her books and putting them on shelves. She put 2 books on the first shelf, 8 books on the second shelf, 32 books on the third shelf, and 128 books on the fourth shelf. What kind of sequence is this?

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Both

Answer

Neither

Question 37

What kind of sequence is this?

2, 3, 5, 8, ...

Accepted Answer

Neither

Answer

Geometric

Answer

Arithmetic

Answer

Both

Question 38

What are the first three terms in a sequence given by a_n=3n-2

Accepted Answer

1,4,7

Answer

-2,1,4

Answer

1,4,7,10

Answer

-2,1,4,7

Question 39

What is an arithmetic sequence?

Accepted Answer

sequence that has a common difference

Answer

sequence that has a common ratio

Answer

a sequence that has a common difference and ratio

Answer

might as well just give up

Question 40

What is an arithmetic sequence?

Accepted Answer

sequence that has a common difference

Answer

sequence that has a common ratio

Answer

a sequence that has a common difference and ratio

Answer

might as well just give up

Question 41

What is the formula for an arithmetic sequence?

Accepted Answer

a_n=d(n-1)+a_{1 and}a_n=dn+a₀

Answer

a_n=dn+a₀

Answer

a_n=d(n-1)+a₁

Answer

only the orange one

Question 42

what is a geometric sequence?

Accepted Answer

A sequence that  has a common ratio

Answer

A sequence that has a common difference

Answer

only the orange one

Answer

A sequence that has a common ratio and a common difference

Question 43

What is the formula for a geometric sequence?

Accepted Answer

a_n=a₁(r)^(n-1)

Answer

a_n=d_n+a₀

Answer

a_n=d(n-1)+a_{1 and}a_n=d_n+a₀

Answer

a_n=a₁(r)^(n-1) and a_n=d_n+a₀

Question 44

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 45

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 46

Determine whether the sequence is arithmetic, geometric, or neither.

Accepted Answer

geometric

Answer

arithmetic

Answer

neither

Question 47

Find the common ratio: 16, 8, 4, 2, ...

Accepted Answer

r = 1/2

Answer

r = 2

Answer

r = 8

Answer

r = 1/4

Question 48

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

Accepted Answer

yes

Answer

no

Question 49

Find the 22nd term of the following sequence:
5, 8, 11, ...

Accepted Answer

68

Answer

14

Answer

63

Answer

71

Question 50

Which formula is used to find the recursive equation for arithmetic sequences?

Accepted Answer

a_n = a_(n-1) + d

Answer

a_n = a_(n-1) * r

Answer

a_n = a₁ + d(n-1)

Answer

a_n = a₁ * r^n-1

Question 51

Which formula is used to find the explicit equation for geometric sequences?

Accepted Answer

a_n = a₁ * r^n-1

Answer

a_n = a_(n-1) + d

Answer

a_n = a_(n-1) * r

Answer

a_n = a₁ + d(n-1)

Question 52

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
-14, -11, -8, -5, ...

Accepted Answer

Arithmetic
Common Difference: 3

Answer

Arithmetic
Common Difference: -3

Answer

Geometric
Common Ratio: 4

Answer

Geometric
Common Ratio: 3

Question 53

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
-6, -18, -54...

Accepted Answer

Geometric
Common Ratio: 3

Answer

Arithmetic
Common Difference: 3

Answer

Geometric
Common Ratio: -3

Answer

Arithmetic
Common Difference: 12

Question 54

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
256, 64, 16, 4,...

Accepted Answer

Geometric
Common Ratio: ¹/₄

Answer

Arithmetic
Common Difference: 4

Answer

Arithmetic
Common Difference: ¹/₄

Answer

Geometric
Common Ratio: -4

Question 55

What is the rule in this sequence?

200, 100, 50, 25....

Accepted Answer

Divide by 2

Answer

Multiply by 2

Answer

Subtract 100

Answer

Subtract 50

Question 56

What is the missing number in this sequence?

9, 54, ____, 1,944

Accepted Answer

324

Answer

6

Answer

256

Answer

540

Question 57

What is the missing number in this sequence?

6, ____, 18, 24

Accepted Answer

12

Answer

6

Answer

10

Answer

15

Question 58

What is the missing number in this sequence?

___, 8, 32, 128

Accepted Answer

2

Answer

4

Answer

1

Answer

3

Question 59

Write the recursive form for the sequence:
200, 150, 112.5...

Accepted Answer

f(1)=200, f(n)=f(n-1)0.75

Answer

f(200),  f(n)=f(200)0.75

Answer

f(1),  f(n)=f(n-1)75

Question 60

What is the recursive rule for the sequence:
2, 6, 18, 54...

Accepted Answer

f(1)=2, f(n)=f(n-1)3

Answer

f(3), f(n)=f(n-1)2

Answer

f(2), f(n)=f(n-1)4

Answer

f(1)=3, f(n)=f(n-1)2

Question 61

Does this graph show an arithmetic or a geometric sequence?

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Neither

Answer

Both

Question 62

Select any statement that is true concerning the sequence 5, 10, 20, 40, 80...

Accepted Answer

The sequence is geometric

Accepted Answer

The explicit formula is a_n = 5(2)^n-1

Accepted Answer

The sequence can be modeled by an exponential function.

Answer

The sequence is arithmetic

Answer

The sequence can be modeled by a linear function.

Question 63

Discrete or Continuous?

Accepted Answer

Discrete

Answer

Continuous

Question 64

In discrete functions, the x-values...

Accepted Answer

Can only be whole numbers

Answer

Can be all numbers

Answer

Can only be decimals

Arithmetic and Geometric Sequences Review with Explicit Formulas

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