Download number patterns

NUMBER PATTERNS
Questions to ask
One of the important things you need to do when faced with a pattern, is to know what
questions to ask:






Is there a constant difference or ratio between numbers?
If the difference or ratio is not constant, is there a pattern in the differences?
Does the pattern alternate?
Do you need to take two or more numbers together to make a sequence?
Are powers of numbers involved?
Is there no pattern at all, in that some other criteria must be involved, e.g. prime
numbers, days in the month?
Strategies
When looking for the pattern in a list of numbers either look for the pattern that connects
the number with the number before it.

e.g. 2, 4, 6, 8, 10, . . . . .
before it)
(each number is two more than the one
Or, look for a pattern that connects each term with its position number in the sequence.

Number
1
2
3
4
....
100
Term
2
4
6
8
....
2  100 = 200
Number pattern exercises
Fill in the gaps in each pattern:
1) , , , , , , ____, ____, ____, . . . . . . .
2) , , , , , , ____, ____, ____, . . . . . .
3) , , , , , , ____, ____, ____, . . . . . . .
4) 1, -1, 2, -2, 3, ____, ____, ____, . . . . . . .
1
Updated Feb 2013
5) 2, 4, 6, 8, 10, ____, ____, ____, . . . . . . .
6) 1, 3, 5, 7, 9, ____, ____, ____, . . . . . . .
7) 3, 6, 9, 12, 15, ____, ____, ____, . . . . . . .
8) 1, 4, 9, 16, 25, ____, ____, ____, . . . . . . .
9) 1, 5, 9, 13, 17, ____, ____, ____, . . . . . . .
10) 3, 3, 6, 9, 15, 24, 39, ____, ____, ____, . . . . . . .
11) 1, 2, 6, 24, 120, 720, ____, ____, ____, . . . . . . .
12) 1, 2, 3, 5, 7, 11, 13, 17, ____, ____, ____, . . . . . . .
13) 2, 6, 18, ____, ____, ____, . . . . . . .
14) 0, 6½, 13, ____, ____, ____, . . . . . . .
15) ____, ____, ____, 1, 2, 4, ____, ____, ____, . . . . . . .
16) 1000, 100, 10, 1,
1
, ____, ____, ____, . . . . . . .
10
17) –3, -2, ____, 0, 1, ____, ____, . . . . . . .
18) ____, ____, ____, 7, 11, 15 . . . . . . .
19) -4, -2, 0, 2, ____, ____, ____, . . . . . . .
20) 1, 7, 13, ____, ____, ____, . . . . . . .
21) 8, 4, 2, ____, ____, ____, . . . . .. .
22) 130, 122, 114, ____, ____, ____, . . . . . . .
23) 1, 2, 4, 5, 7, 8, ____, ____, ____, . . . . . . .
24) ____, ____, ____, 23, 32, 41 . . . . . . .
25) 5, 13, 21, ____, ____, ____, . . . . . . .
26) ____, 50, 25, 12½, ____, ____, . . . . . . .
2
Updated Feb 2013
27) ____, ____, 79, ____, 61, ____, 43, . . . . . . .
28) –13, -7, -1, ____, 11, ____, ____, ____, . . . . . . .
29) 250, 50, 10, ____, ____, ____, . . . . . . .
30) 135, 45, 15, ____, ____, ____, . . . . . . .
31) –7, -5, -2, 2, 7, ____, ____, ____, . . . . . . .
32) 2, 5, 11, 23, ____, ____, ____, . . . . . . .
33) ____. 100, 20, 4, 0.8, ____, ____, . . . . . .
34)
Number
1
2
3
4
....
Term
1
3
5
7
....
a) Find (2  1) - 1
b) Find (2  2) - 1
c) Find (2  3) - 1
d) The 100th term in the sequence is given by (2  ___) - 1
e) The 100th term in the sequence is _____?
35)
Number
1
2
3
4
....
n
....
100
....
Term
2
5
10
17
....
___
....
___
....
a) Find 12 + 1
b) Find 22 + 1
c) Find 32 + 1
d) The 100th term in the sequence is given by ____2 + 1
3
Updated Feb 2013
e) The 100th term in the sequence is _____?
f) The nth term in this sequence is given by ____2 + 1
g) What is the 13th term?
36)
Number
1
2
3
4
5
6
....
n
....
Term
3
7
11
15
19
23
....
___
....
a) Find (4  1) - 1 = _____
b) Find (4  2) - 1 = _____
c) Find (4  3) - 1 = _____
d) Find (4  6) - 1 = _____
e) nth term = _____
f) 31st term = _____
37)
Number
1
2
3
4
5
6
....
n
....
Term
0
2
4
6
8
10
....
___
....
a) What is the nth term?
b) What is the 71st term?
4
Updated Feb 2013
Number pattern Solutions
1) , , , , , , , , . . . . . . .
2) , , , , , , , , , . . . . . .
3) , , , , , , , , , . . . . . . .
4) 1, -1, 2, -2, 3, -3, 4, -4, . . . . . .
5) 2, 4, 6, 8, 10, 12, 14, 16, . . . . . . .
even numbers
6) 1, 3, 5, 7, 9, 11, 13, 15, . . . . . . .
odd numbers
7) 3, 6, 9, 12, 15, 18, 21, 24, . . . . . . .
add 3
8) 1, 4, 9, 16, 25, 36, 49, 64, . . . . . . n2
9) 1, 5, 9, 13, 17, 21, 25, 29, . . . . . . .
add 4
10) 3, 3, 6, 9, 15, 24, 39, 63, 102, 165, . . . . . . add two previous numbers
11) 1, 2, 6, 24, 120, 720, 5040, 40 320, 362 880, . . n! = n(n-1)(n-2)(n-3)….1
12) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, . . . . prime numbers
13) 2, 6, 18, 54, 162, 486, . . . . . . . previous number  3
14) 0, 6½, 13, 19½ , 26, 32½ , . . . . . . .
add 6½
1
15) 8 , ¼ , ½ , 1, 2, 4, 8, 16, 32, . . . . . . .double
16) 1000, 100, 10, 1,
1 1
1
1
,
,
,
, . . . . . . . divide by 10
10 100 1000 10000
17) –3, -2, -1, 0, 1, 2, 3, . . . . . . .add 1
18) -5, -1, 3, 7, 11, 15. . . . . . .add 4
19) -4, -2, 0, 2, 4, 6, 8, . . . . . . .add 2
20) 1, 7, 13, 19, 25, 31, . . . . . . . add 6
21) 8, 4, 2, 1, ½ , ¼ , . . . . . . .divide by 2
5
Updated Feb 2013
22) 130, 122, 114, 106, 98, 90, . . . . . . .subtract 8
23) 1, 2, 4, 5, 7, 8, 10, 11, 13, . . . . . . .
add 1, add 2
24) -4, 5, 14, 23, 32, 41 . . . . . . add 9
25) 5, 13, 21, 29, 37, 45, . . . . . . .add 8
26) 100, 50, 25, 12½, 6¼, 3 18 , . . . . . . .divide by 2
27) 97, 88, 79, 70, 61, 52, 43, . . . . . . .subtract 9
28) –13, -7, -1, 5, 11, 17, 23, 29, . . . . . . .add 6
29) 250, 50, 10, 2,
2
5
,
2
25
30) 135, 45, 15, 5,
5
3
,
5
9
, . . . . . . .divide by 5
, . . . . . . .divide by 3
31) –7, -5, -2, 2, 7, 13, 20, 28, . . . . . . .add 2, add 3, add 4, add 5, . . . .
32) 2, 5, 11, 23, 47, 95, 191, . . . . . . .
add 3, add 6, add 12, add 24, . . . .
33) 500. 100, 20, 4, 0.8, 0.16, 0.032, . . . . . . divide by 5
34) a) 1
b) 3
c) 5
d) (2  100) - 1
e) 199
35) a) 2
f) n2 + 1
b) 5
g) 170
c) 10
d) 1002 + 1
e) 10001
36) a) 3
f) 123
b) 7
c) 11
d) 23
37) a) (2  n) - 2
b)
140
6
Updated Feb 2013
e) (4  n) - 1
Number Squares
Possible strategies



Do the rows or columns add up to the same total?
Is one row or column a combination of the other rows or columns?
Does the pattern involve the individual digits of the numbers?
Number Squares Exercises
1.
3.
5.
4
20
5
?
8
6
7
5
6
4
5
8
3
2
9
6
54
9
7
1
4
8
49
7
6
2
7
?
2
3
8
4
2
3
2.
4.
12
3
24
12
16
33
14
5
16
2
9
27
53
2
19
2
2
?
71
45
19
?
10
3
7
2
3
4
24
5
1
4
1
5
2
10
8
2
6
6
3
2
36
9
7
?
2
2
1
?
6.
7
Updated Feb 2013
7.
9.
12
3
4
16
2
27
?
1
3
5
7
8
2
5
8
11
9
3
7
11
15
4
9
14
?
?
13
6
7
9
12
?
8.
10.
2
?
13
?
?
12
1
10
11
3
?
11. Each symbol represents a digit
The sums of each row and column are given
What is the sum of the digits along the diagonal, starting in the top lefthand corner?




5




7




14




11
10
8
8
11
?
8
Updated Feb 2013
Fill in the spaces in the following, identifying the row and column rules in each case.
12.
3
6
12
1
4
2
4
14.
6
7
1
10
25
3
1
2
24.
18
12
21.
8
4
2
6
2
2
19
2
4
14
10
12
15
4
16
4
16
8
256
6553
6
6
18
2
6
30
23.
2
17
25.
7
15
12
4
8
3
7
1
9
Updated Feb 2013
16
12
4
12
3
2
10
14
7
8
19.
6
6
10
6
6
4
22.
17.
8
1
9
12
6
6
20.
48
100
9
5
50
50
50
18.
15.
9
5
12
9
0
16.
13.
13
Number Square solutions
1.
1,
column 2  column 1 = column 3
2.
5,
all rows add up to 20
3.
4,
column 1 column 2 = column 3
4.
27,
the individual digits in columns 1, 2 & 3 add up to the number in column 4
5.
2,
column1 – column 2 = column 3
6.
4,
column 1  column 2  column 3 = column 4
7.
3,
column 1  column 2 = column 3
8.
19,
column 2 + column 3 - column 1 = column 4
9.
8, 11, 5, all rows, columns and diagonals add up to 27
10. 21, 23, 22,
 = 1,  = 2,  = 3,  = 4
11. 10,
12.
all rows, columns and diagonals add up to 36
3
6
12
1
2
2
4
13.
12
9
4
15
13
10
7
8
9
6
3
cols: 2 row1 = row2 + row 3
14.
cols: -4, +6
4
0
6
7
3
5
1
cols: -3
15.
48
16
8
9
12
4
2
7
6
2
1
cols: 3, 2 rows: 3, 2
rows: +3, -2
10
Updated Feb 2013
rows: - 2 ,– 4
16.
5
10
50
25
50
50
100
17.
6
2
1
250
12
4
2
500
24
8
4
cols: 2, 5 rows: 5, 2
18.
cols: 3, 2 rows: 2, 2
6
9
6
5
8
6
9
19.
19
14
17
5
12
7
10
6
17
12
15
cols: +3, -3 rows: -1, +1
20.
cols: -5, +3 rows: -7, +5
3
6
12
1
2
4
2
4
8
21.
cols: 2, 2 rows: 3, 2
22.
cols: -5, +3
16
4
16
16
256
256
65536
2
3
6
30
1
2
2
4
6
18
10
3
1
2
6
20
2
4
12
23.
cols: 2, 3 rows: 3, 2
19
14
17
12
7
17
12
25.
4
8
10
3
7
16
15
15
1
5
13
rows: -7, +5
cols: +4, +8
11
Updated Feb 2013
4
cols: number rows: number
cols: 2, 5 rows: 3, 2
24.
2
rows: -1, -2
2