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arithmetic and geometric sequence

Total questions: 31

Worksheet time: 1hrs 12mins

Name
Class
Date
1.
Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}
a)
Arithmetic
b)
Geometric
c)
Neither
2.
Is this sequence Arithmetic, Geometric, or Neither?
{2, 9, 7, 14, 12, 19, ... }
a)
Arithmetic
b)
Geometric
c)
Neither
3.
What is the 38th term of this sequence?
{26, 22, 18, 14, ... }
a)
-4
b)
10
c)
-122
d)
174
4.
What is the common ratio of this sequence?
{2, 10, 50, 250, ... }
a)
1,250
b)
5
c)
10
d)
50
5.
Dividing by 12 is the same as ...
a)
× 12
b)
÷ 1/12
c)
× 1/12
d)
+ 12
6.
What is the common difference in this sequence?
{48, 32, 16, 0, ... }
a)
1/2
b)
2
c)
-8
d)
-16
7.
Is this sequence Arithmetic, Geometric, or Neither?
{14, 22, 30, 38, .. }
a)
Arithmetic
b)
Geometric
c)
Neither
8.
Find the 10th term of this sequence:
{96, 48, 24, 12, ... }
a)
3/16
b)
1/2
c)
6
d)
3
9.
What is the common ratio in this sequence? 
{96, 48, 24, 12, ... }
a)
1/2
b)
2
c)
12
d)
24
10.
Dividing by 5 is the same as...
a)
× 5
b)
÷ 1/5
c)
- 5
d)
× 1/5
11.
An auditorium has 80 rows of seats and the number of seats per row increases at a constant rate.  If there are 32 seats in the 8th row, and 68 seats in the 20th row, how many seats are in the last row?
a)
240
b)
248
c)
272
d)
320
12.
What is a5 in the sequence defined as follows?
an = 5 ⋅ 2(n-1) 
a)
a5 = 160
b)
a5 = 40
c)
a5 = 10
d)
a5 = 80
13.
What are the first three terms of the sequence defined by the following equation?
an = 7 + (n - 1)5
a)
7, 35, 175
b)
7, 2, -3
c)
12, 17, 22
d)
7, 12, 17
14.
What is the 15th term of the sequence an = -3n+50
a)
95
b)
-5
c)
5
d)
-95
15.
What is the 10th term of the sequence an = 20-2n
a)
40
b)
-20
c)
7
d)
0
16.
What kind of sequence is the pattern 400, 200, 100, 50, 25, ...?
a)
Arithmetic
b)
Geometric
c)
Neither
17.

The explicit formula for a sequence is an = 5 − 3n. What is the value of a22 ?

a)

a22 = -61

b)

a22 = 61

c)

a22 = -1

d)

a22 = -51

18.

Identify the common difference or ratio.

3, 7, 11, 15, ...

a)

Ratio, -4

b)

Difference, -4

c)

Difference, 4

d)

Ratio, 4

19.
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?
a)
Geometric
b)
Arithmetic
c)
Both
d)
Neither
20.

Which EXPLICIT function describes the sequence 3, 7, 11, 15, ...?

a)

f(1)=3; f(n)=f(n-1)+4

b)

f(1)=4; f(n)=f(n-1)+3

c)

f(x)=3x+4

d)

f(x)=4x-1

21.

Which EXPLICIT function describes the sequence 500, 250, 125, ... ?

a)

f(1)= 500; f(n)=f(n-1)*1/2

b)

500×(1(2))n−1500\times\left(\frac{1}{\left(2\right)}\right)^{_{n-1}}

c)

500(2)(n−1)500\left(2\right)^{\left(n-1\right)}

d)

1000(1(2))(n−1)1000\left(\frac{1}{\left(2\right)}\right)^{\left(n-1\right)}

22.

The sequence 28, 34, 40, 46, 52, ..., 88 has 11 terms. Find the sum of the 11 terms.

a)

550

b)

610

c)

638

d)

288

23.

Find Sn for the given series:

a1=22

d=-8

n=21

a)

1911

b)

-2346

c)

-1449

d)

-1218

24.

Determine the sum of the first 10 terms of the sequence 2, 5, 8, ...

a)

310

b)

155

c)

170

d)

50

25.

Find the sum of first 12 terms of the following sequence:

5, 8, 11, ...

(a)  

26.
Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint:  Write your formula and then simplify it.)
a)
an=2+6n
b)
an=-6+6n
c)
an=6n-4
d)
an=4-6n
27.
Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint:  Write your formula and then simplify it.)
a)
an=2+6n
b)
an=-6+6n
c)
an=6n-4
d)
an=4-6n
28.

How many terms are there in the series  ∑k=3133k+1\sum_{k=3}^{13}3k+1  

a)

13

b)

11

c)

10

29.

Write 1 + 2 + 3 + ... + 10


using sigma notation

a)

∑d=19d\sum_{d=1}^9d

b)

∑d=110d+1\sum_{d=1}^{10}d+1

c)

∑d=110d\sum_{d=1}^{10}d

30.
Determine the sum of the series written in Sigma Notation. 
a)
5400
b)
2692
c)
2700
d)
2704
31.
Determine the sum of the series written in Sigma Notation. 
a)
45
b)
49
c)
90
d)
47

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