Number Series questions

Number Series questions for competitive exams

Number series questions can be of two types. Picking the odd one out and find the missing number in the sequence.

Number series Type1: Spot the odd one 

In this type of questions, you will be given a number series in which one term doesn't follow the common relation that connects other terms. You have to spot that odd one.

Number series Type2: Find the missing one

In this type of questions, you will be given  a  number series in  which one term is missing. You have to find out that missing term.

Number series can also be classified based on the relation between successive terms. In other words 'how succeeding term is obtained from previous term'.

1.Addition/subtraction number series

In this type of series, succeeding term is obtained by adding/subtracting a particular number to the previous term. To solve this type of question, find the difference between successive terms. These 'differences' will form another series. Solve this 'differences' series first, then you can easily solve the original series.

Example1: Find the next term in the series 6   7    9   13    21    37     ?

Take the difference between successive terms.

· 7-6=1

· 9-7=2

· 13-9=4

· 21-13=8

· 37-21=16

· ?-37

Series formed by 'difference' terms is as follows.

1  2  4   8   16   ?

What comes in place of "?" ?.....Yes it is 32.

By adding 32 to 37 ,you get final answer. Thus answer is 69.

Example2: Spot the odd one in the series 5     6     10    18      35     60

· 6-5=1=1²

· 10-6=4=2²

· 18-10=8

· 35-18=17

^·  60-35=25=5²

Here you can see, no specific relation exist between 10&18 and 18&35.

So 18 is the odd one

Correct series is as follows

 5     6     10    19      35     60

· 6-5=1=1²

· 10-6=4=2²

· 19-10=9=3³

· 35-19=16=4²

· 60-35=25=5²

2.Multiplication /Division number series

In this  type of series succeeding term is obtained by multiplying/dividing previous term by a particular number. To solve this type of question ,find the multiplication factor between terms and write it as a series. Solve these 'multiplication factors' series first. Then you can you can easily solve the original series.

Example1:Find the next term in the series. 3 6 15 45 157. 5 ?

· 6=3*2

· 15=6*2.5

· 45=15*3

· 157.5=45*3.5

Series formed by multiplication factors is 2  2.5   3   3.5   ?

What comes in place of "?" ? It is 4.

So ?=157.5*4=630.

Thus answer is 630.

Example2:Find the odd term in the series.1   2   8    72     1250

· 2=1*1^2

· 8=2*2^2

· 72=8*3^2

Here you can see  multiplication terms form a series 1²    2²   3²   ?.

What comes in place of "?" ?.It is 4². So, 72*4²=1152 comes in place of 1250.Thus odd one is 1250.

3.Combination of Addition/Subtraction and Multiplication /division series

In this type of series succeeding term is obtained by multiplying previous term by a number and adding/subtracting some other number. Like in above cases this multiplying/adding/subtracting number will form a series or a particular pattern. Try to identify the patterns that multiplying/adding/subtracting numbers are following. Then you can easily figure out pattern behind 

original series.

Example: 4     3     4     9    32

At first, by looking at the series you may not be able to figure out relation between successive terms. As already said, actually there exist  no 'specific logic ' to solve number series questions. You need to practice more and more questions, so that your brain will get adapted to these kind of problems. Now lets look into the pattern that above series is following.

· 3=4*1-1

· 4=3*2-2

· 9=4*3-3

· 32=9*4-4

You can see that multiplying terms and subtracting terms follows a certain pattern.

4:Apart from above categories ,series can be formed by adding/subtracting multiple numbers with previous term to get succeeding term.

Example:1   2     7     50     2507

· 2=1² +1

· 7=2² + 3

· 50=7² +5

· 2507=50² +7