Each question in this set shows a series of numbers with a question mark standing in for the missing number. Look carefully at the numbers you are given and work out the rule connecting them: it could be a fixed amount added or taken away each time, a fixed multiplier or divisor, a gap between the numbers that grows or shrinks by a steady amount, two separate series running through the same list one term at a time, or a rule that builds each number from the two numbers just before it. Once you have spotted the rule, pick the option, A to E, that carries the series on correctly. Exactly one option fits in each question; the other four are built around mistakes that are easy to make, such as using the wrong step size, stopping a growing gap one step too soon, or losing track of which of two interleaved series you are following. Look at the worked example first, then answer the questions in order - they begin gently and become more demanding as the set goes on.
Worked example. 3, 7, 11, 15, 19, ?
A) 20 B) 21 C) 22 D) 23 E) 25 Answer: D) 23. Each number in the series is 4 more than the number before it (add 4 each time): 3, 7, 11, 15, 19. So the next number after 19 is 19 + 4 = 23, which is option D. Option A (20) adds only 1; option B (21) adds 2; option C (22) adds 3; option E (25) adds 6, overshooting the true difference.
1
Find the next number in this series.
5, 11, 17, 23, 29, ?
A) 33
B) 34
C) 35
D) 36
E) 38
(Total for Question 1 is 1 mark)
2
Find the next number in this series.
3, 10, 17, 24, 31, ?
A) 36
B) 37
C) 38
D) 39
E) 41
(Total for Question 2 is 1 mark)
3
Find the next number in this series.
50, 44, 38, 32, 26, ?
A) 17
B) 19
C) 20
D) 21
E) 22
(Total for Question 3 is 1 mark)
4
Find the next number in this series.
2, 6, 18, 54, ?
A) 90
B) 108
C) 156
D) 162
E) 216
(Total for Question 4 is 1 mark)
5
Find the next number in this series.
128, 64, 32, 16, ?
A) 4
B) 6
C) 8
D) 10
E) 12
(Total for Question 5 is 1 mark)
6
Find the next number in this series.
6, 15, 24, 33, 42, ?
A) 49
B) 50
C) 51
D) 52
E) 53
(Total for Question 6 is 1 mark)
7
Find the next number in this series.
1, 3, 6, 10, 15, ?
A) 18
B) 19
C) 20
D) 21
E) 22
(Total for Question 7 is 1 mark)
8
Find the next number in this series.
1, 8, 27, 64, 125, ?
A) 36
B) 186
C) 206
D) 216
E) 343
(Total for Question 8 is 1 mark)
9
Find the next number in this series.
5, 9, 16, 26, 39, ?
A) 49
B) 52
C) 54
D) 55
E) 57
(Total for Question 9 is 1 mark)
10
Find the next number in this series.
80, 75, 67, 56, 42, ?
A) 23
B) 25
C) 26
D) 28
E) 32
(Total for Question 10 is 1 mark)
11
Find the next number in this series.
4, 5, 9, 14, 23, 37, ?
A) 46
B) 58
C) 60
D) 61
E) 74
(Total for Question 11 is 1 mark)
12
Find the next number in this series.
8, 13, 10, 15, 12, 17, ?
A) 12
B) 14
C) 15
D) 20
E) 22
(Total for Question 12 is 1 mark)
13
Find the next number in this series.
4, 50, 9, 44, 14, 38, ?
A) 13
B) 18
C) 19
D) 20
E) 32
(Total for Question 13 is 1 mark)
14
Find the next number in this series.
6, 90, 12, 80, 24, 70, ?
A) 36
B) 46
C) 48
D) 60
E) 96
(Total for Question 14 is 1 mark)
15
Find the next number in this series.
3, 8, 18, 38, 78, ?
A) 118
B) 156
C) 157
D) 158
E) 160
(Total for Question 15 is 1 mark)
16
Find the next number in this series.
10, 17, 31, 59, 115, ?
A) 171
B) 224
C) 226
D) 227
E) 230
(Total for Question 16 is 1 mark)
17
Find the next number in this series.
4, 7, 13, 25, 49, ?
A) 61
B) 73
C) 93
D) 97
E) 101
(Total for Question 17 is 1 mark)
18
Find the next number in this series.
1024, 256, 64, 16, ?
A) 1
B) 2
C) 4
D) 8
E) 12
(Total for Question 18 is 1 mark)
19
Find the next number in this series.
10, 12, 17, 20, 22, 27, ?
A) 29
B) 30
C) 31
D) 32
E) 33
(Total for Question 19 is 1 mark)
20
Find the next number in this series.
90, 60, 86, 53, 82, 46, ?
A) 39
B) 75
C) 77
D) 78
E) 79
(Total for Question 20 is 1 mark)
21
Find the next number in this series.
2, 4, 12, 48, 240, ?
A) 432
B) 1200
C) 1400
D) 1440
E) 1680
(Total for Question 21 is 1 mark)
22
Find the next number in this series.
2, 1, 3, 4, 7, 11, ?
A) 4
B) 15
C) 17
D) 18
E) 22
(Total for Question 22 is 1 mark)
23
Find the next number in this series.
3, 60, 6, 50, 12, 41, ?
A) 18
B) 24
C) 26
D) 33
E) 48
(Total for Question 23 is 1 mark)
24
Find the next number in this series.
5, 53, 77, 89, 95, ?
A) 98
B) 99
C) 101
D) 104
E) 107
(Total for Question 24 is 1 mark)
25
Find the next number in this series.
2, 3, 4, 9, 8, 27, ?
A) 12
B) 14
C) 16
D) 32
E) 81
(Total for Question 25 is 1 mark)
26
Find the next number in this series.
2, 3, 10, 26, 72, ?
A) 98
B) 144
C) 190
D) 196
E) 200
(Total for Question 26 is 1 mark)
Mark scheme · EP.V16B Number Series: Practice Set 2
Question 1
B1 C) 35 - each term increases by 6 (5, 11, 17, 23, 29, 35)
Answer: C) 35
Question 2
B1 C) 38 - each term increases by 7 (3, 10, 17, 24, 31, 38)
Answer: C) 38
Question 3
B1 C) 20 - each term decreases by 6 (50, 44, 38, 32, 26, 20)
Answer: C) 20
Question 4
B1 D) 162 - each term is multiplied by 3 (2, 6, 18, 54, 162)
Answer: D) 162
Question 5
B1 C) 8 - each term is divided by 2 (128, 64, 32, 16, 8)
Answer: C) 8
Question 6
B1 C) 51 - each term increases by 9 (6, 15, 24, 33, 42, 51)
Answer: C) 51
Question 7
B1 D) 21 - the amount added increases by 1 each time (+2, +3, +4, +5, +6), so 15+6=21
Answer: D) 21
Question 8
B1 D) 216 - these are the cube numbers 1x1x1, 2x2x2, 3x3x3, 4x4x4, 5x5x5, 6x6x6 (1, 8, 27, 64, 125, 216)
Answer: D) 216
Question 9
B1 D) 55 - the difference between terms increases by 3 each time (4, 7, 10, 13, 16), so 39+16=55
Answer: D) 55
Question 10
B1 B) 25 - the amount subtracted increases by 3 each time (5, 8, 11, 14, 17), so 42-17=25
Answer: B) 25
Question 11
B1 C) 60 - each term is the sum of the two before it (4, 5, 9, 14, 23, 37, 60)
Answer: C) 60
Question 12
B1 B) 14 - the pattern alternates +5 then -3 (8, 13, 10, 15, 12, 17, 14), so 17-3=14
Answer: B) 14
Question 13
B1 C) 19 - two series are woven together: one adding 5 each time (4, 9, 14, ?) and one subtracting 6 each time (50, 44, 38); the next term continues the first series to give 19
Answer: C) 19
Question 14
B1 C) 48 - two series are woven together: one doubling each time (6, 12, 24, ?) and one subtracting 10 each time (90, 80, 70); the next term continues the first series to give 48
Answer: C) 48
Question 15
B1 D) 158 - each term is double the previous term, plus 2 (3, 8, 18, 38, 78, 158)
Answer: D) 158
Question 16
B1 D) 227 - each term is double the previous term, minus 3 (10, 17, 31, 59, 115, 227)
Answer: D) 227
Question 17
B1 D) 97 - the difference between terms doubles each time (3, 6, 12, 24, 48), so 49+48=97
Answer: D) 97
Question 18
B1 C) 4 - each term is divided by 4 (1024, 256, 64, 16, 4)
Answer: C) 4
Question 19
B1 B) 30 - the additions repeat in a cycle of +2, +5, +3 (10, 12, 17, 20, 22, 27, 30), so 27+3=30
Answer: B) 30
Question 20
B1 D) 78 - two series are woven together: one subtracting 4 each time (90, 86, 82, ?) and one subtracting 7 each time (60, 53, 46); the next term continues the first series to give 78
Answer: D) 78
Question 21
B1 D) 1440 - each term is multiplied by an increasing integer (x2, x3, x4, x5, x6): 2, 4, 12, 48, 240, 1440
Answer: D) 1440
Question 22
B1 D) 18 - each term is the sum of the two before it (2, 1, 3, 4, 7, 11, 18)
Answer: D) 18
Question 23
B1 B) 24 - two series are woven together: one doubling each time (3, 6, 12, ?) and one decreasing by a shrinking amount (60, 50, 41); the next term continues the doubling series to give 24
Answer: B) 24
Question 24
B1 A) 98 - the difference between terms halves each time (48, 24, 12, 6), so 95+3=98
Answer: A) 98
Question 25
B1 C) 16 - two series are woven together: one doubling each time (2, 4, 8, ?) and one tripling each time (3, 9, 27); the next term continues the doubling series to give 16
Answer: C) 16
Question 26
B1 D) 196 - each term is double the sum of the two terms before it: 2x(2+3)=10, 2x(3+10)=26, 2x(10+26)=72, 2x(26+72)=196