Number Series short cut techniques

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A number series can be considered as a collection of numbers in which all the terms are formed according to some particular rule or all the terms follow a particular pattern. The relation of any term to its preceding term will be same through out the series.

You have to find out the rule in which the terms of the series are selected and depending on that rule you have to find out the missing number. There is no definite rule for the series. Generally the series can be of the following types. 

• Prime Series : IN which the terms are the prime numbers in Order
• Ex : 2, 3, 5, 7, 11, 13, _ , 19
• Here the terms of the series are the prime numbers in order. The prime number after 13 is 17. So the answer to this question is 17.

• Alternate Primes : 
• Ex: 2, 5, 11, 17, 23, _, 41
• Here the series is framed by taking the alternative prime numbers. After 23, the prime numbers are 29 and 31. So the answer is 31.

• Every Third number can be the sum of the preceding two numbers:
• Ex : 3, 5, 8, 13, 21
• Here starting from third number
•  3 + 5 = 8
•  5 + 8 = 13
•  8 + 13 = 21
• So, the answer is 13 + 21 = 34

• Every Third number can be the product of the preceeding two numbers
• Ex : 1, 2, 2, 4, 8, 32. _
• Here starting from the third number
• 1 X 2 = 2
• 2 X 2 = 4
• 2 X 4 = 8 
• 4 X 8 = 32
• So, the answer is 8 X 32 = 256
• The difference of any term from its succeding term is constant (either increasing series or decreasing series :
• Ex : 4, 7, 10, 13, 16, 19, _, 25
• Here the difference of any term from its succeding term is 3.
• 7 - 4 = 3
• 10 - 7 = 3
• So, the answer is 19 + 3 = 22

• The difference between two consecutive terms will be either increasing or decreasing by a constant number :
• Ex : 2, 10, 26, 50, 82, _
• Here, The difference between two consecutive terms are
• 10 - 2 = 8
• 26 - 10 = 16
• 50 - 26 = 24
• 82 - 50 = 32
• Here, the difference is increased by 8 (or you can say the multiples of 8). So the next difference will be 40 (32 + 8). So, the answer is 82 + 40 = 122
• Ex : 63, 48, 35, 24, 15, _
• Here, the difference between the two terms are
• 63 - 48 = 15
• 48 - 35 = 13
• 35 - 24 = 11
• 24 - 15 = 9
• Here, the difference is decreased by 2. So, the next difference will be 7. So, the answer is 15 - 7 = 8.

• The difference between two numbers can be multiplied by a constant number :
• Ex : 15, 16, 19, 28, 55, _
• Here, the differences between two numbers are
• 16 - 15 = 1
• 19 - 16 = 3
• 28 - 19 = 9
• 55 - 28 = 27
• Here, the difference is multiplied by 3. So, the next difference will be 81. So, the answer is 55 + 81 = 136

• The difference can be multiplied by numbers which will be increasing by a constant number :
• Ex : 2, 3, 5, 11, 35, _
• The difference between two numbers are
• 3 - 2 = 1
• 5 - 3 = 2
• 11 - 5 = 6
• 35 - 11 = 24
• Here, the differences are multiplied by numbers which are in increasing order.
• Differences are 
• 1
• 1 x 2 = 2
• 2 x 3 = 6
• 6 x 4 = 24
• So, the next difference will be 24 x 5 = 120. So, the answer is 35 + 120 = 155.

• Every succeeding term is got by multiplying the previous term by a constant number or numbers which follow a special pattern. 
• Ex : 5, 15, 45, 135, _
• Here, 5 x 3 = 15
• 15 x 3 = 45
• 45 x 3 = 135
• So, the answer is 135 x 3 = 405.
• Ex : 2, 10, 40, 120, 240, _
• Here, 2 x 5 = 10
• 10 x 4 = 40
• 40 x 3 = 120
• 120 x 2 = 240
• So, the answer is 240 x 1 = 240

• In certain series the terms are formed by various rule (miscellaneous rules). By keen observation you have to find out the rule and the appropriate answer.
• Ex : 4, 11, 31, 90, _
• Terms are,
• 4 x 3 - 1 = 11
• 11 x 3 - 2 = 31
• 31 x 3 - 3 = 90
• So, the answer will be 90 x 3 - 4 = 266
• Ex : 3, 5, 14, 55, _
• Terms are,
• 3 x 2 - 1 = 5
• 5 x 3 - 1 = 14
• 14 x 4 - 1 = 55
• So, the answer will be 55 x 5 - 1 = 274
• Ex : 3, 7, 23, 95, _
• Terms are,
• 3 x 2 + 1 = 7
• 7 x 3 + 2 = 23
• 23 x 4 + 3 = 95
• So, the answer will be 95 x 5 + 4 = 479
• Ex : 6, 17, 38, 79, _
• Terms are,
• 6 x 2 + 5 = 17
• 17 x 2 + 4 = 38
• 38 x 2 + 3 = 79
• So, the answer is 79 x 2 + 2 = 160

As we already told, there is no rule or logic to solve these type of problems. Only practice can make your brain sharp to understand the logic in a quick glance. so do as many problems on number series as possible.

Now lets do some Examples on Number Series >>

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