Number series are mathematical sequences that follow a certain rule based on elementary arithmetic operations. A series or sequence of numbers is given, with 1 or more missing terms. One must find the pattern (or find the logic) that connects the numbers forming the series, apply the logic or pattern to find out the missing number(s). Some of the commonly asked patterns are listed below-
Series with
Same Difference
3, 6, 9, 12, _ (15 is the next term obtained by adding 3 to previous term)
Ans 15
24, 20, 16, 12, _ (8 is the next term obtained by reducing 4 from the previous term)
Ans 4
Increasing Difference
3, 4, 6, 9, __ (The difference between successive numbers in increasing by 1, 2, 3,… So, the missing term 13 obtained by adding 4 to the previous term 9)
Ans 13
25, 24, 22, 19, _ (The difference between successive numbers is increasing by 1, 2, 3…. So, the missing term 15 obtained by reducing 4 from the previous term 19)
Ans 15
Decreasing Difference
2, 9, 15, 20, __ (The difference between successive numbers in decreasing by 7, 6, 5… so, the missing term 24 obtained by adding 4 to the previous term 20)
Ans 24
30, 22, 15, 9, __ (The difference between successive numbers is decreasing by 8, 7, 6…. so, the missing term 4 obtained by reducing 5 from the previous term 9)
Ans 4
Difference Doubles or Halves
5, 9, 17, 33, __. (The difference between every two successive numbers is double of the difference between previous pair of successive terms 9-5=4, 17-9=8, 33-17=16…., so, the missing term 65 is obtained by adding 32 to the previous term 33)
Ans:65
120, 80, 60, 50, _ (The difference between successive numbers is half of the previous difference i.e.120-80= 40, 80-60=20, 60-10=50.., so the missing term 45 is obtained by reducing 5 from the previous term 50)
Ans: 45
Multiplication or Division By Same Number
3, 6, 12, 24, _ (The successive numbers obtained by multiplying the previous number by 2, so the missing term 48 is obtained by multiplying 24 by 2)
Ans: 48
729, 243, 81, 27, _ (The successive numbers are obtained by dividing the previous number by 3, so the missing term 9 is obtained by dividing 27 by 3)
Ans: 9
Multiplication and Division is Done By Increasing Numbers
2, 4, 12, 48, _ (The successive numbers are obtained by multiplying the previous numbers by 2,3,4,…. so the missing term 240 is obtained by multiplying 48 by 5)
Ans: 240
120, 60, 20, 5, _ (The successive numbers are obtained by dividing the previous numbers
by 2,3,4,…, so the missing term 1 is obtained by dividing 5 by 5)
Ans: 1
Previous Two Numbers Add Up to Third Number
1,1, 2, 3, 5, _ (The successive numbers are obtained by adding the previous two numbers, so, the missing term 8 is obtained by adding 3 and 5)
This is also known as Fibonacci series.
Ans: 8
Successive Number is Product of Previous Two Numbers
1, 3, 3, 9, 27,_ (The successive numbers are obtained by multiplying the previous two numbers, so the missing term 243 obtained by product of 9 and 27)
Ans: 243
Mixed Series or Series formed by combination of two series
The missing term belongs to series 2: Ans- 32 is obtained by multiplying 16 by 2
Combination of mathematical operations
2, 3, 8, 27, __
The missing term 112 is obtained by following the mathematical operation (27 X 4) + 4
Ans: 112
Miscellaneous Patterns
Number series and patterns can come in an unimaginable variety. Lets try a few more patterns
Some examples:
Question : Write the missing term from the given options.
- 2, 9, 30, 68, ___, 222.
a)112 b) 124 c) 130 d) 180
Solution: 13+1=2 , 23 + 2=10 , 33+3=30 , 43+4=68 , 53+5=130 , 63+6=222
2. 165, 275, 385, 495, ___ , 660
a)585 b) 561 c) 530 d) 541
Solution: Each number of the series has digit at 1s place +digit at 100s place= digit at 10s place. Only option b) fits the pattern 5+1=6.
Ans b) 561
3. 143,77, 35, 15, ___
a)5 b) 8 c) 6 d) 0
Solution: 13×11=143, 11×7=77, 7×5=35, 5×3=15, 3×2=6 . Product of two successive prime numbers taken in descending order.
Ans: c) 6
