Each question shows a series of numbers with a question mark in place of the missing number. Study the numbers already given and work out the rule that links them together: the rule might be a constant amount added or subtracted, a constant multiplier or divisor, a difference that itself increases or decreases, two series woven together term by term, or a rule linking each number to the two numbers before it. Once you have worked out the rule, choose the option, A to E, that continues the series correctly. Only one option is correct in each question, and each wrong option is designed to match a common slip such as using the wrong difference, stopping the pattern too early, or muddling two interleaved series. Study the worked example below before you begin, then work through the questions in order: they start off easier and get harder as you go.
Worked example. 2, 4, 6, 8, 10, ?
A) 11 B) 12 C) 13 D) 14 E) 16 Answer: B) 12. Each number in the series is 2 more than the number before it (add 2 each time): 2, 4, 6, 8, 10. So the next number after 10 is 10 + 2 = 12, which is option B. Option A (11) adds only 1; option C (13) adds 3; option D (14) adds 4; option E (16) adds 6, doubling the true difference.
1
Find the next number in this series.
4, 8, 12, 16, 20, ?
A) 22
B) 24
C) 25
D) 26
E) 28
(Total for Question 1 is 1 mark)
2
Find the next number in this series.
2, 6, 10, 14, 18, ?
A) 20
B) 22
C) 23
D) 24
E) 26
(Total for Question 2 is 1 mark)
3
Find the next number in this series.
45, 40, 35, 30, 25, ?
A) 15
B) 18
C) 20
D) 21
E) 22
(Total for Question 3 is 1 mark)
4
Find the next number in this series.
3, 9, 27, 81, ?
A) 162
B) 240
C) 243
D) 324
E) 729
(Total for Question 4 is 1 mark)
5
Find the next number in this series.
96, 48, 24, 12, ?
A) 3
B) 4
C) 6
D) 8
E) 10
(Total for Question 5 is 1 mark)
6
Find the next number in this series.
1, 5, 9, 13, 17, ?
A) 19
B) 20
C) 21
D) 22
E) 25
(Total for Question 6 is 1 mark)
7
Find the next number in this series.
2, 3, 5, 8, 12, ?
A) 13
B) 15
C) 16
D) 17
E) 18
(Total for Question 7 is 1 mark)
8
Find the next number in this series.
1, 4, 9, 16, 25, ?
A) 30
B) 32
C) 35
D) 36
E) 49
(Total for Question 8 is 1 mark)
9
Find the next number in this series.
2, 6, 12, 20, 30, ?
A) 36
B) 40
C) 42
D) 44
E) 50
(Total for Question 9 is 1 mark)
10
Find the next number in this series.
3, 8, 15, 24, 35, ?
A) 44
B) 45
C) 46
D) 48
E) 50
(Total for Question 10 is 1 mark)
11
Find the next number in this series.
100, 90, 81, 73, 66, ?
A) 58
B) 59
C) 60
D) 61
E) 64
(Total for Question 11 is 1 mark)
12
Find the next number in this series.
5, 10, 20, 40, 80, ?
A) 100
B) 120
C) 150
D) 160
E) 320
(Total for Question 12 is 1 mark)
13
Find the next number in this series.
243, 81, 27, 9, ?
A) 1
B) 3
C) 4
D) 5
E) 6
(Total for Question 13 is 1 mark)
14
Find the next number in this series.
1, 1, 2, 3, 5, 8, ?
A) 10
B) 11
C) 12
D) 13
E) 14
(Total for Question 14 is 1 mark)
15
Find the next number in this series.
10, 13, 11, 14, 12, 15, ?
A) 9
B) 12
C) 13
D) 16
E) 18
(Total for Question 15 is 1 mark)
16
Find the next number in this series.
3, 6, 11, 18, 27, ?
A) 33
B) 35
C) 36
D) 38
E) 40
(Total for Question 16 is 1 mark)
17
Find the next number in this series.
2, 5, 11, 23, 47, ?
A) 70
B) 93
C) 94
D) 95
E) 96
(Total for Question 17 is 1 mark)
18
Find the next number in this series.
5, 20, 8, 16, 11, 12, ?
A) 8
B) 13
C) 14
D) 15
E) 17
(Total for Question 18 is 1 mark)
19
Find the next number in this series.
3, 30, 6, 27, 9, 24, ?
A) 11
B) 12
C) 13
D) 15
E) 21
(Total for Question 19 is 1 mark)
20
Find the next number in this series.
1, 2, 6, 24, 120, ?
A) 144
B) 480
C) 600
D) 720
E) 840
(Total for Question 20 is 1 mark)
21
Find the next number in this series.
2, 3, 5, 9, 17, ?
A) 25
B) 31
C) 32
D) 33
E) 34
(Total for Question 21 is 1 mark)
22
Find the next number in this series.
7, 9, 13, 21, 37, ?
A) 53
B) 68
C) 69
D) 70
E) 101
(Total for Question 22 is 1 mark)
23
Find the next number in this series.
3, 4, 7, 11, 18, 29, ?
A) 36
B) 45
C) 46
D) 47
E) 48
(Total for Question 23 is 1 mark)
24
Find the next number in this series.
2, 100, 4, 50, 8, 25, ?
A) 10
B) 12
C) 16
D) 32
E) 50
(Total for Question 24 is 1 mark)
25
Find the next number in this series.
2, 5, 10, 17, 26, 37, ?
A) 45
B) 48
C) 49
D) 50
E) 51
(Total for Question 25 is 1 mark)
Mark scheme · EP.V16 Number Series
Question 1
B1 B) 24 - each term increases by 4 (4, 8, 12, 16, 20, 24)
Answer: B) 24
Question 2
B1 B) 22 - each term increases by 4 (2, 6, 10, 14, 18, 22)
Answer: B) 22
Question 3
B1 C) 20 - each term decreases by 5 (45, 40, 35, 30, 25, 20)
Answer: C) 20
Question 4
B1 C) 243 - each term is multiplied by 3 (3, 9, 27, 81, 243)
Answer: C) 243
Question 5
B1 C) 6 - each term is divided by 2 (96, 48, 24, 12, 6)
Answer: C) 6
Question 6
B1 C) 21 - each term increases by 4 (1, 5, 9, 13, 17, 21)
Answer: C) 21
Question 7
B1 D) 17 - the amount added increases by 1 each time (+1, +2, +3, +4, +5), so 12+5=17
Answer: D) 17
Question 8
B1 D) 36 - these are the square numbers 1x1, 2x2, 3x3, 4x4, 5x5, 6x6 (1, 4, 9, 16, 25, 36)
Answer: D) 36
Question 9
B1 C) 42 - the difference between terms increases by 2 each time (4, 6, 8, 10, 12), so 30+12=42
Answer: C) 42
Question 10
B1 D) 48 - the difference between terms increases by 2 each time (5, 7, 9, 11, 13), so 35+13=48
Answer: D) 48
Question 11
B1 C) 60 - the amount subtracted decreases by 1 each time (10, 9, 8, 7, 6), so 66-6=60
Answer: C) 60
Question 12
B1 D) 160 - each term doubles the one before it (5, 10, 20, 40, 80, 160)
Answer: D) 160
Question 13
B1 B) 3 - each term is divided by 3 (243, 81, 27, 9, 3)
Answer: B) 3
Question 14
B1 D) 13 - each term is the sum of the two before it (1, 1, 2, 3, 5, 8, 13)
Answer: D) 13
Question 15
B1 C) 13 - the pattern alternates +3 then -2 (10, 13, 11, 14, 12, 15, 13), so 15-2=13
Answer: C) 13
Question 16
B1 D) 38 - the difference between terms increases by 2 each time (3, 5, 7, 9, 11), so 27+11=38
Answer: D) 38
Question 17
B1 D) 95 - each term is double the previous term plus 1 (2, 5, 11, 23, 47, 95)
Answer: D) 95
Question 18
B1 C) 14 - two series are woven together: one adding 3 each time (5, 8, 11, ?) and one subtracting 4 each time (20, 16, 12); the next term continues the first series to give 14
Answer: C) 14
Question 19
B1 B) 12 - two series are woven together: one adding 3 each time (3, 6, 9, ?) and one subtracting 3 each time (30, 27, 24); the next term continues the first series to give 12
Answer: B) 12
Question 20
B1 D) 720 - each term is multiplied by an increasing integer (x2, x3, x4, x5, x6): 1, 2, 6, 24, 120, 720
Answer: D) 720
Question 21
B1 D) 33 - each term is double the previous term minus 1 (2, 3, 5, 9, 17, 33)
Answer: D) 33
Question 22
B1 C) 69 - the difference between terms doubles each time (2, 4, 8, 16, 32), so 37+32=69
Answer: C) 69
Question 23
B1 D) 47 - each term is the sum of the two before it (3, 4, 7, 11, 18, 29, 47)
Answer: D) 47
Question 24
B1 C) 16 - two series are woven together: one doubling each time (2, 4, 8, ?) and one halving each time (100, 50, 25); the next term continues the doubling series to give 16
Answer: C) 16
Question 25
B1 D) 50 - the difference between terms increases by 2 each time (3, 5, 7, 9, 11, 13), so 37+13=50