## Sequence and Series Questions and Solutions : Logical Reasoning

• 1. Which number would replace underline mark in the series?
2, 5, 10, 17, ---, 37
A.) 27
B.) 24
C.) 26
D.) 28

Here the difference between the consecutive terms is increase by 2
5 - 2 = 3,
10 - 5 = 5,
17 - 10 = 7,
then 17 + 9 = 26.

• 2. Which number would replace underline mark in the series?
1, 6, 26,_____, 426.
A.) 86
B.) 76
C.) 106
D.) 96

Here the difference between the consecutive terms is multiplied by 4.
The difference of the two consecutive numbers is 5, 20, .....
5 × 4 = 20
20 × 4 = 80
26 + 80 = 106.

• 3. Which number would replace underline mark in the series?
1, 20, 58, ____, 191.
A.) 105
B.) 115
C.) 111
D.) 116

Here the difference between the two consecutive terms is 19, 38, 57, 76
58 + 57 = 115

• 4. 2, 10, 40, 120,____
A.) 240
B.) 360
C.) 470
D.) 210

Here the series is a multiplication series.
The order of the multiplication is ×5, ×4, ×3, ×2
120 × 2 = 240

• 5. 18 21 25 18 29 33 18
What numbers should come next ?
A.) 43 18
B.) 41 44
C.) 37 41
D.) 38 41

This is a simple addition series with a random number, 18, interpolated as every third number.
In the series, 4 is added to each number except 18, to arrive at the next number

• 6. 20 20 17 17 14 14 11 What numbers should come next ?
A.) 8 8
B.) 8 9
C.) 11 8
D.) 8 9s

This is a simple subtraction with repetition series.
It begins with 20, which is repeated, then 3 is subtracted, resulting in 17, which is repeated, and so on.
Rule = (1st no) (1st no) (1st no - 3 = 2nd no) (2nd no repeat) (2nd no - 3 = 3rd no) (3rd no repeat). . .
Now (20) (20) (20 - 3 = 17) (17) (17 - 3 = 14) (14) (14 - 3 = 11) (11) (11 - 3 = 8) (8)
So the answer is e = 11 8.

• 7. 3 13 18 23 28 33
What number should come next?
A.) 38 43
B.) 37 42
C.) 38 44
D.) 39 44

In this simple addition series, each number is 5 greater than the previous number.
Rule = (1st no) (1st no + 5 = 2nd no) (2nd no + 5 = 3rd no) . . .
Now (3) (3 + 5 = 8) (8 + 5 = 13) (13 + 5 = 18) (18 + 5 = 23) (23 + 5 = 28) (28 + 5 = 33) (33 + 5 = 38) (38 + 5 = 43)
So the answer is c = 38 43

• 8. Look at this series: 1000, 200, 40, . . .
What number should come next?
A.) 10
B.) 8
C.) 9
D.) 12

This is a simple division series.
Each number is divided by 5.
Rule = (1st number / 5 = 2nd number) (2nd number / 5 = 3rd number)....
Now, (1000 / 5 = 200), (200 / 5 = 40), (40 / 5 = 8)...
So answer is a = 8.

• 9. Look at this series: 7, 10, 8, 11, 9, 12, . . .
What number should come next?
A.) 7
B.) 10
C.) 15
D.) 18

This is a simple alternating addition and subtraction series.
In the first pattern, 3 is added;
In the second pattern, 2 is subtracted.
Rule =(1st number) (1st number + 3 = 2nd number) (2nd number - 2 = 3rd number) (3rd number + 3 = 4th number)
Now (7) (7 + 3 = 10) (10 - 2 = 8) (8 + 3 = 11) (11 - 2 = 9) (9 + 3 = 12) (12 - 2 = 10)...
So the answer is b = 10.

• 10. 1, 2, 3, 10, ____, 9802
A.) 199
B.) 999
C.) 99
D.) 298

12 + 1 = 2

22 - 1 = 3

32 + 1 = 10

102 - 1 = 99.

• 11. 2, 10, 26, 50, ___, 122.
A.) 82
B.) 90
C.) 80
D.) 62

Here the series of the form (12 + 1), (32 + 1), (52 + 1), .......

• 12. Look at this series: 14, 28, 20, 40, 32, 64, . . .
What number should come next ?
A.) 52
B.) 56
C.) 86
D.) 98

This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
Rule = (1st no.) (1st x 2 = 2nd no.) (2nd - 8 = 3rd no.) (3rd x 2 = 4th no.)....
Now (14) (14 x 2 = 28) (28 - 8 = 20) (20 x 2 = 40) (40 - 8 = 32) (32 x 2 = 64) (64 - 8 = 56)...
So the answer is b = 56.

• 13. Look at this series: 5.2, 4.8, 4.4, 4, . . .
What number should come next?
A.) 3
B.) 3.6
C.) 3.5
D.) 3.3

In this simple subtraction series, each number decreases by 0.4.
Rule = (1st no.) (1st no. - 0.4 = 2nd no.) (2nd no. - 0.4 = 3rd number)...
Now (5.2) (5.2 - 0.4 = 4.8) (4.8 - 0.4 = 4.4) (4.4 - 0.4 = 4) (4 - 0.4 = 3.6) ...
So the answer is d = 3.6

• 14. 84 78 72 66 60 54 48
What number should come next ?
A.) 44 34
B.) 42 36
C.) 42 32
D.) 40 34

In this simple subtraction series, each number is 6 less than the previous number.
Rule = (1st number) (1st no - 6 = 2nd no.) (2nd no - 6 = 3rd no). . .
Now (84) (84 - 6 = 78) (78 - 6 = 72) (72 - 6 = 66) (66 - 6 = 60) (60 - 6 = 54) (54 - 6 = 48) (48 - 6 = 42) (42 - 6 = 36).
So the answer is b = 42 36

• 15. Look at this series: 3, 4, 7, 8, 11, 12, . . .
What number should come next ?
A.) 7
B.) 10
C.) 15
D.) 20

This alternating addition series begins with 3;
then 1 is added to give 4;
then 3 is added to give 7;
then 1 is added, and so on.
Rule = (first number + 1) (second number + 3) (third number + 1) (fourth number + 3)...
Now The series is 3, 4, 7, 8, 11, 12...
(3 + 1 = 4), (4 + 3 = 7), (7 + 1 = 8), (8 + 3 = 11), (11 + 1 = 12) (12 + 3 = 15)...
So the answer is d = 15.

• 16. Look at this series: 31, 29, 24, 22, 17, . . .
What number should come next?
A.) 15
B.) 14
C.) 13
D.) 12

This is a simple alternating subtraction series, which subtracts 2, then 5.
Rule = (first number - 2) (second number - 5) (third number - 2) (fourth number - 5)...
Now The series is 31, 29, 24, 22, 17, . . .
(31 - 2 = 29), (29 - 5 = 24), (24 - 2 = 22), (22 - 5 = 17), (17 - 2 = 15)...
So the answer is a = 15.

• 17. Find the wrong number in the series.
1, 2, 6, 15, 31, 56, 91
A.) 31
B.) 71
C.) 81
D.) 91

The difference odd the two consecutive numbers are
1, 4, 9, 16, 25, 35.
+12, +22, +32,+42,+52,+62
Here 35 is is wrong. wrong answer 91

• 18. Find the wrong number in the series.
2, 5, 10, 17, 26, 37, 50, 64
A.) 5
B.) 26
C.) 64
D.) 17

12 + 1, 22 + 1, 32 + 1 ..........82 + 1 = 65

But 64 has been given here. So our wrong number is 64

• 19. Find the missing number in the following series.
512, 256, 64, 32, ?
A.) 16
B.) 4
C.) 8
D.) 10

512/2 = 256
256/4 = 64
64/2 = 32
32/4 = 8.

• 20. Find the missing number in the following series.
2, 3, 6, 15, 45, ?
A.) 95
B.) 105.5
C.) 147
D.) 157.5

2 × 1.5 = 3
3 × 2 = 6
6 × 2.5 = 15
15 × 3 = 45
45 × 3.5 = 157.5

• 21. Find the missing number in the following series.
376, 188, 47, 23.5, ?
A.) 7.8
B.) 6.5
C.) 5.8
D.) None of these

367/2 = 188
188/4 = 47
47/2 = 23.5
23.5/4 = 5.8

• 22. Find the missing number in the following series.
1050, 506, 236, 105, ?
A.) 45.5
B.) 45
C.) 42.5
D.) 41.5

1050/2 = 525 - 19 = 506
506/2 = 253 - 17 = 236
236/2 = 118 - 13 = 105
105/2 = 52.5 - 11 = 41.5

• 23. Find the missing number in the following series.
12, 53, 207, 618, ?
A.) 1324
B.) 1432
C.) 1234
D.) 1124

12 × 5 - 7 = 53
53 × 4 - 5 = 207
207 × 3 - 3 = 618
618 × 2 - 2 = 1234.

• 24. Look at the series 3, 3/2, 3/4, 3/6 … what number should come next?
A.) 3/8
B.) 3/12
C.) 1
D.) 3/18

3/8

• 25. Look at the series 2, 3, 5, 8, 12….. What number should come next?
A.) 14
B.) 15
C.) 16
D.) 17