A number series is a sequence of numbers written in a certain pattern from left to right. We have to detect/find the pattern that is followed in the series to solve the series questions. There are various types of number series. Firstly, we have to find out the type of the series So that we can find the wrong/missing term in the series.
Types of series
There can be following types of series
The series, in which the next term is obtained by adding or subtracting a specific number to the previous term, is known as difference series. In this, series is in increasing or decreasing order and the difference between consecutive terms is equal.
Example: Find out the missing term in series 1, 6, 11, 16... 26.
Sol. Here, every next term is obtained by adding 5 to the previous term.
Required term = 16 + 5 = 21
Example: Find out the missing term in the series 82, 74, 66, 58... 42.
Sol. Here, every next number is 8 less than the previous number. So, required number = 58–8 = 50
In this type of series, the series is made of perfect squares in a certain way and asks to find the missing/wrong series.
Ex. 22 = 4, 32= 9, 42= 16, 52= 25, 62= 36, 72= 49
In this type of series, the series is made of perfect cubes in a certain way and asks to find the missing/wrong series.
Example: 13= 1, 23= 8, 33= 27, 43= 64, 53= 125
The number which is divisible by 1 and itself is called a prime number. In this type of series, the series is formed by using a prime number is called prime number series.
Example: Find out the next term in the series 7, 11,13,17,19,
In this type of series, each term of a series is obtained by multiplying a number with the previous term is called a multiplication series.
Note: Number which is multiplied to consecutive terms, can be fixed or variable
Example: Find out the missing term in series 3, 6, 12, 24, 48... 192. Sol. Here, every next number is double
the previous number. So, required number = 48 x 2 = 96
In alternating series, successive terms increase and decrease alternately. There is a combination of two different series.
Two different operations are performed on successive terms alternately.
Example: Find the next term in the series 1, 3, 5, 6, 9, 9,?
First series 1, 5, 9, 13 – there is difference of 4 in each term.
Second series 3, 6, 9, 12- there is a difference of 3 in each term.
This type of series contains more than one different pattern in a series which arranged in alternatively in a single series or follow any non-conventional rule is called mixed series.
Example: 5, 6, 14, 45, 184, ?
5×1+1= 6
6×2+2= 14
14×3+3= 45
45×4+4= 184
184×5+5= 925
The missing term is 925
Q1. 1. 9.5, 29, 105, 428, 2165, 13020
(A) 9.5 (B) 29
(C) 105 (D) 2165
(E) 428
Q2. 2. 7, 26, 61, 120, 203, 321, 481
(A) 26 (B) 61
(C) 120 (D) 321
(E) 481
Q3. 20, 72, 150, 272, 600, 1056
(A) 20 (B) 72
(C) 150 (D) 272
(E) 600
Q4. 4, 11, 41, 126, 1492, 4481
(A) 11 (B) 41
(C) 126 (D) 1492
(E) 4481
Q5. 3, 9, 30, 129, 651, 3913
(A) 3 (B) 9
(C) 30 (D) 129
(E) 651
Q6. 5, 15, 55, 233, 1195, 7195
(A) 55 (B) 233
(C) 1195 (D) 7195
(E) None of these
Q7. 1, 9, 27, 64, 125, 216, 343
(A) 9 (B) 27
(C) 64 (D) 125
(E) 343
Q8. 3, 14, 29, 49, 75, 110, 149
(A) 14 (B) 29
(C) 75 (D) 110
(E) None of these
Q9. 2, 6, 12, 20, 30, 40, 56
(A) 6 (B) 12
(C) 20 (D) 30
(E) 40
Q10. 7, 12, 19, 27, 39, 52, 67
(A) 12 (B) 19
(C) 27 (D) 39
(E) 52
Q11. 15, 23, 35, 54, 79, 110, 147
(A) 35 (B) 23
(C) 140 (D) 110
(E) 79
Q12. 11, 15, 24, 42, 65, 101, 150
(A) 11 (B) 15
(C) 42 (D) 101
(E) None of these
Q13. Which is the next number in the given number series?
13. 1, 4, 27, 16, 125, 36, ?
(A) 45 (B) 64
(C) 225 (D) 343
(E) None of these
Q14. 6, 4, 5, 11, 39, 189, ?
(A) 456 (B) 840
(C) 1080 (D) 1127
(E) None of these
Q15. 11, 6, 7, ? , 68, 552
(A) 12 (B) 16
(C) 18 (D) 24
(E) None of these
Q16. 3, 15, 35, ? , 99, 143
(A) 63 (B) 65
(C) 72 (D) 84
(E) None of these
Q17. 3, 8, 18, 33, ?, 88, 118
(A) 45 (B) 53
(C) 65 (D) 68
(E) None of these
Q18. 1, 14, 39, 84, ?, 258, 399
(A) 130 (B) 145
(C) 148 (D) 155
(E) None of these
Q19. 13, 18, 28, ? , 88, 168, 188
(A) 36 (B) 40
(C) 48 (D) 54
(E) None of these
Q20. 5, 30, 140, ? , 4380, 30695
(A) 196 (B) 325
(C) 725 (D) 884
(E) None of these
1. C
2. D
3. C
4. A
5. C
6. B
7. A
8. D
9. E
10. C
11. B
12. C
13. D
14. D
15. B
16. A
17. B
18. D
19. C
20. C
