Dear Reader,

In this post, you will see the basics behind number series problems and ways to crack them.

Number series problems are one of the easiest topics in competitive exams. You can expect them in question papers of Bank, SSS, UPSC exams, etc.

In a series, the numbers will be connected to each other by a common idea/pattern. After discovering the pattern and you have to identify the missing number. (There can also be odd man out type questions)

Below are some of the commonly occurring patterns in such problems.

- Simple addition/subtraction/multiplication
- Squares or cubes
- Prime numbers
- Any other complex series using a combination of the above patterns.

### Few Tips to Identify Pattern.

In few cases, a quick glance will help you determine the nature (squares, cubes, primes, etc.) of a series. In other situations, the below tips will help you.

- Find the difference between consecutive numbers. You may come to either of the below conclusions:

a) If the difference is increasing or decreasing rapidly, it could be a square/cube/multiplication series.

b) If the difference is increasing or decreasing slowly, it could be an addition or subtraction series - In most of the cases, the series will not be straightforward. The differences between the consecutive terms themselves will form a sub-series. (You will understand these types after seeing the below examples.)

Let us start solving few number series questions.

**Question 1:**

10, 11, 15, 24, 40, ?

**Solution:**

The difference between successive numbers are 1, 4, 9 and 16 i.e 1^{2}, 2^{2}, 3^{2} and 4^{2}.

Note: Here the differences form a square sub-series.

10 + 1^{2} = 11

11 + 2^{2} = 15

15 + 3^{2} = 24

24 + 4^{2} = 40

So the next number will be 40 + 5^{2} = 65.

**Question 2:**

28, 30, 33, 38, 45, ?

**Solution:**

The difference between numbers in the series is 2, 3, 5 and 7.

(By seeing 3, 5 and 7 in a hurried manner, you may think the next number will be 9. But that is wrong. The pattern/idea should be applicable from begin of the series.)

2,3,5 and 7 form a prime numbers based sub-series. The next number of this sub-series will be 11.

Hence answer will be 45 + 11 = 56

**Question 3: **

3, 5, 15, 45, 113,?

**Solution:**

Sub-series formed by the difference between consecutive terms is 2, 10, 30 and 68.

This sub-series follows the below pattern.

1^{3} + 1, 2^{3} + 2, 3^{3} + 3 and 4^{3} + 4.

So the next term of the difference sub-series will be 5^{3} + 5 = 130. Final answer will be 113 + (5^{3} + 5) = 113 + 130 = 243.

Hence answer is 243.

To help you understand better, below is a detailed representation of the entire series.

3 + (1^{3} + 1) = 3 + 2 = 5

5 + (2^{3} + 2) = 5 + 10 = 15

15 + (3^{3} + 3) = 15 + 30 = 45

45 + (4^{3} + 4) = 45 + 68 = 113

113 + (5^{3} + 5) = 113+130 = 243.

This stuff is great. Thanks for providing these rules. Huge help