 ## Number Series

Theory

Number Series is one of the more important topics for IBPS PO. Quite a few questions come from this topic every year. In these questions, a series of numbers along with a missing number is given and the student is asked to find out the missing number.

Theory

For a given question, examine the difference between adjacent numbers. A number of times, the difference between adjacent numbers in a series is constant.

Tip

Even if the difference between the numbers is dynamic rather than constant, there is still a clear logical rule. In such a case, see if the difference of numbers is in Arithmetic Progression – first difference is 1, second difference is 2 and so on.

Theory

Examine if there is a multiplication pattern between the numbers. For example, in the series: 1, 2, 4, 8, 16, … each number is twice the previous number.

Tip

Most of the times when the numbers in the series follow a multiplicative pattern, the multiplicative number is either 2 or ½.

Theory

If the numbers do not follow an addition or multiplication pattern, check if you can use a rule that involves two or more basic arithmetic functions ( +, -, x, / ). For example, in the series 2, 4, 8, 6, 3,… the rule is: add 2 to the first number to get the second number, then multiply the second number by 2 to get the third number, subtract 2 from the third number to get the fourth number and divide the fourth number by 2 to get the fifth number.

Theory

Identifying the wrong number in a series

Sometimes questions are asked on identifying the wrong number in a series. This is more difficult than finding the missing number because in this case, the wrong number might mislead the thought process. One way of solving this is by assuming one of the numbers to be wrong and trying to find the logic connecting the other numbers. If a proper logic is not found, then consider another number to be wrong and repeat the process.

Tip

While solving questions on identifying the wrong number in a series, try to see if you get a proper logic for the series by going from left to right. If not, then try to find the logic by going from right to left.

Theory

In some questions, two series are given, with the first series being complete and the second series being incomplete. In these questions, the student has to identify the logic that the numbers of the first series follow and apply the same logic to the numbers of the second series. These questions are slightly easier compared to the other two types of questions.

Solved Example

What comes next in the series: 3, 5, 9, 15, 23, ____

a) 31
b) 33
c) 35
d) None of the above

Explanation:
The difference between the first two numbers is 2. The difference between the 3rd and 4th numbers is 4. The difference between the 4th and 5th numbers is 6 and so on.

So, the difference between 23 and the next number should be 10.
So, the next number in the series is 23+10 = 33

Solved Example

Consider the following two series:

1, 2, 6, 24, 120, …
2, a, b, c, d, …

What is the value of ‘c’?

a) 144
b) 12
c) 48
d) 4

Explanation:
In the first series, the second number is twice the first number; the third number is three times the second number; the fourth number is four times the third number and so on.
The same rule has to be applied to the numbers in the second series also.

So, a = 2*2 = 4
b = 4*3 = 12
c = 12*4 = 48

So, the value of ‘c’ is 48.