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Number patterns and pythagoras

Total questions: 75

Worksheet time: 2hrs 34mins

Name
Class
Date
1.

Find the rule the pattern is using:

11,9,7,5,3

a)

Subtract 2

b)

Divide 3

c)

Add 3

d)

Subtract 3

2.

Find the rule the pattern is using:

3,9,15,21,27

a)

Multiply 3

b)

Add 4

c)

Add 6

d)

Multiply 10

3.

Which choice uses the same addition rule as the pattern shown?

5,12,19,26,33

a)

9,18,27,36,45

b)

6,15,24,33,42

c)

9,16,23,30,37

d)

9,14,19,24,29

4.

Which choices uses the same subtraction rule as the pattern shown?

35,25,18,11,4

a)

37,28,19,10,1

b)

36,29,22,15,8

c)

43,34,25,16,7

d)

13,10,7,4,1

5.

What is the SIXTH number in this pattern?

13,16,19,22

a)

28

b)

25

c)

31

d)

22

6.

What is the CORRECTLY written rule for this pattern?

12,21,30,39,48,57

a)

Start at 12. Add 18

b)

Start at 3. Add 9

c)

Start at 21. Subtract 9

d)

Start at 12. Add 9

7.

What is the FOURTH number in this pattern?

47,53,59

a)

71

b)

65

c)

77

d)

64

8.

Find the rule the pattern is using:

448,112,28,7

a)

Divide 4

b)

Subtract 336

c)

Divide 5

d)

Subtract 84

9.

In the pattern: 4, 7, 10, 13, 16,... what is the 10th term?


Assume that 4 is the 0th term

(a)  

10.

In the pattern: 4, 7, 10, 13, 16,... what is the 8th term?


Assume that 4 is the 1st term

(a)  

11.

In the pattern: 4, 7, 10, 13, 16,... what would the 50th term be?


Assume that 4 is the 0th term

a)

150

b)

151

c)

154

d)

50

12.

In the pattern: 4, 7, 10, 13, 16,... what would the term number be if our term is 22?


Assume that 4 is the 1st term

a)

term 5

b)

term 6

c)

term 7

d)

term 8

13.

In the pattern: 4, 7, 10, 13, 16,... which expressions would represent the pattern with 4 as our 1st term?

a)

1 + 3x

b)

3x

c)

3x + 1

d)

3x + 4

14.

In the pattern: 4, 7, 10, 13, 16,... which expressions would represent the pattern with 4 as our 0th term?

a)

3x + 4

b)

4 + 2x + x

c)

3x + 1

d)

3x - 4

15.

In the pattern: 7, 4, 1, -2, -5,...

What would the 6th term be?


Assume that 7 is our 1st term

a)

-5

b)

-8

c)

-6

d)

-11

16.

In the pattern: 7, 4, 1, -2, -5,...

What would the term number be if the term was -38?


Assume that 7 is our 1st term

a)

15

b)

14

c)

17

d)

16

17.

What expression would represent the following pattern:

7, 4, 1, -2, -5,...


Assume that 7 is our 1st term

a)

-3x + 10

b)

-3x

c)

-3x + 7

d)

-3x - 10

18.

What expression would represent the following pattern:

7, 4, 1, -2, -5,...


Assume that 7 is our 0th term

a)

-3x + 10

b)

-3x

c)

-3x + 7

d)

-3x - 10

19.

In the following pattern, what would the next term be?


1, 4, 9, 16, 25,...

(a)  

20.

In the following pattern: 6, 6, 6, 6, 6, ...


Select ALL the statements that are true

a)

An equation to represent the pattern would be: y = 6

b)

The pattern is NOT changing. It is staying constant

c)

The pattern is changing by adding 1

d)

The pattern would be a horizontal line if graphed

e)

An equation to represent the pattern would be: y = 6x

21.

Which pattern below is best represented by the expression:

7x - 2

a)

5, 7, 9, 11, 13

b)

5, 12, 19, 26, 33

c)

7, 14, 21, 28, 35

d)

-2, -9, -16, -23, -30

22.

Which pattern below is best represented by the expression:

x2 + 1

a)

1, 4, 9, 16

b)

2, 3, 4, 5, 6

c)

2, 5, 10, 17

23.

How do you feel about being able to write expressions for patterns?

a)

I'm a pro at it!

b)

I feel confident about it but I also know I need more practice

c)

I am slowly getting it

d)

I don't understand it at all!

24.
The sum of 6 and x
a)
x + 6
b)
6/x
c)
x + 4
d)
6x
25.
Evaluate 2r + 1      if   r = 3
a)
6
b)
5
c)
7
d)
8
26.
Evaluate the expression.    Let     c = 3     d = 2
3c + 7d
a)
27
b)
21
c)
29
d)
23
27.
Evaluate expression: 5a + b for a= 6 and b= 3
a)
33
b)
36
c)
30
d)
59
28.
Match the equation to a correct statement.
a)
He charged $5 every hour.
b)
He left 5 hours ago.
c)
he started with $5
d)
he bought 5 lemons
29.
Total pay is $10 to show up
and $7  for every hour worked. Which of the following statements is true?
a)
The initial value is 7
b)
the initial value is 10
c)
the rate of change is 10
d)
the initial value is 17
30.
How many blocks will be in the 4th term?
a)
The next term will have 16 blocks
b)
The next term will have 15 blocks.
c)
The next term will have 14 blocks.
d)
This is the end of the pattern.
31.
How many counters would come next?
a)
5
b)
7
c)
9
d)
11
32.
How many cubes would be in the next shape?
a)
15
b)
16
c)
17
d)
18
33.
If you extended the pattern, how many dots would come next?
a)
16
b)
20
c)
25
d)
30
34.
What is the rule for this pattern?
32,36,40,44
a)
add 4
b)
multiply 2
c)
subtract 4
d)
divide by 2
35.

7, 14, 21, 28, 35

a)

Linear

b)

Non-Linear

36.

Start at 6, add 10 each time.

a)

Linear

b)

Non-linear

37.

1, 5, 25, 125, 625

a)

Linear

b)

Non-Linear

38.
a)

Linear

b)

Non-Linear

39.
a)

Linear

b)

Non-Linear

40.
a)

Linear

b)

Non-Linear

41.

Which of these is an arithmetic pattern?

a)

10, 20, 30, 60

b)

5, 10, 15, 20

c)

25, 26, 28, 30

d)

2, 4, 6, 10

42.

Is this an arithmetic pattern? 3, 6, 9, 15

a)

Yes

b)

No

43.

Select the BEST description for this pattern: 100, 200, 300, 400, 500

a)

The numbers are decreasing by 100 each time.

b)

The numbers are increasing by 100 each time.

c)

The numbers are increasing by 1 each time.

d)

The numbers are getting higher by 1 each time.

44.

Is this an arithmetic pattern? 9, 18, 27, 35, 41

a)

Yes

b)

No

45.

Describe the pattern. 4, 8, 12, 16, 20, 24

a)

The numbers are decreasing.

b)

The numbers are increasing by 2 each time.

c)

The numbers are increasing by 4 each time.

d)

The numbers are decreasing by 4 each time.

46.

Describe the arithmetic pattern. 24, 20, 16, 12, 8

a)

The numbers are decreasing by 10 each time.

b)

The numbers are increasing by 5 each time.

c)

The numbers are decreasing by 4 each time.

d)

The numbers are adding 5 each time.

47.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
48.
Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...
a)
-1, 7, 15
b)
-5, 2, 9
c)
3, 12, 21
d)
-65, -73, -81
49.
Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.
a)
an = 4n + 29
b)
an = -4n + 25
c)
an = -4n + 29
d)
an = 4n + 25
50.
Given the recursive formula, find the first four terms:
an = an-1 + 5
a1 = -16
a)
-16, -21, -26, -31
b)
5, -11, -27, -43
c)
-16, -80, -500, -200
d)
-16, -11, -6, -1
51.
Find the 22nd term of the following sequence:
5, 8, 11, ...
a)
14
b)
68
c)
63
d)
71
52.
Identify the common difference.
3, 7, 11, 15, ...
a)
6
b)
5
c)
4
d)
2
53.
What is the rule (explicit equation) for the nth term given 
60, 55, 50, 45, ...
a)
an= -5+60n
b)
an= -5n+55
c)
an= -5n+65
d)
an= 5n+55
54.
Write the explicit rule for the arithmetic sequence
12, 10, 8, 6, ...
a)
an = 12n - 14
b)
an = 2n - 14
c)
an = -2n + 14
d)
an = -12n + 14
55.
Find the first term of the given sequence:
a14=68
d=3
a)
14
b)
20
c)
26
d)
29
56.

Is the sequence arithmetic: 0.2, 0.22, 0.222, 0.2222, ...

a)

Yes

b)

No

57.
Which of the following is not an Arithmetic Progression?
a)
1, 4, 7, 10, .....
b)
-5, -2, 1, 4, .....
c)
3, 7, 12, 16, ......
d)
11, 14, 17, 20, .....
58.

The 10th term of the AP: 5, 8, 11, 14, ... is

a)

32

b)

35

c)

38

d)

25

59.

The salary of Reena in 1st year, 2nd year, 3rd year, 4th year with a starting salary of Rs.8000 with an annual increment of Rs.500. What will be her salary in the 7th year

a)

10,000

b)

10,500

c)

11,000

d)

11,500

60.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
61.
Find the 10th term.
a)
16
b)
12
c)
21
d)
30
62.

The next term of an AP  7\sqrt{7}  , 28\sqrt{28}  , 63\sqrt{63}  ,......is 

a)

 70\sqrt{70}  

b)

 84\sqrt{84}  

c)

 98\sqrt{98}  

d)

 112\sqrt{112}  

63.

If the nth term of an AP is (2n+1) then the sum of its first three terms is

a)

6n+3

b)

15

c)

12

d)

21

64.

If 4, x1,x2,x3,28 are in AP then x3 is ______

a)

19

b)

23

c)

22

d)

cannot be determined.

65.

The 5th term of an AP is -3 and its common difference is -4. The sum of its first 10 terms is_________

a)

50

b)

-50

c)

30

d)

-30

66.

The common difference of the AP  1p\frac{1}{p} , 1−pp\frac{1-p}{p}  , 1−2pp\frac{1-2p}{p}  ........is

a)

p

b)

-p

c)

-1

d)

1

67.

Which term of an AP 72, 63, 54, ...... is 0 ?

a)

8th

b)

9th

c)

10th

d)

11th

68.

The sum of first n odd natural numbers is _____

a)

2n-1

b)

2n+1

c)

n2

d)

n2 - 1

69.
Which of the following is not an Arithmetic Progression?
a)
1, 4, 7, 10, .....
b)
-5, -2, 1, 4, .....
c)
3, 7, 12, 16, ......
d)
11, 14, 17, 20, .....
70.
Find the first term of the given sequence:
a14=68
d=3
a)
14
b)
20
c)
26
d)
29
71.
Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.
a)
an = 4n + 29
b)
an = -4n + 25
c)
an = -4n + 29
d)
an = 4n + 25
72.
Create the explicit formula for the sequence:
2, 8, 14, ...
a)
an=2+6n
b)
an=-6+6n
c)
an=6n-4
d)
an=4-6n
73.
What is the first positive term of the sequence:  -9, -5, -1, .......
a)
5
b)
4
c)
3
d)
1
74.
Can the common difference of Arithmetic Progression be negative?
a)
YES. POSSIBLE
b)
NO. NOT POSSIBLE
75.
Which of the following is not an Arithmetic Progression?
a)
1, 4, 7, 10, .....
b)
-5, -2, 1, 4, .....
c)
3, 7, 12, 16, ......
d)
11, 14, 17, 20, .....

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