Number Series

Introduction

Number series refers to a series of numbers arranged after following some logical pattern. The number series questions are common in competitive exams like UGC NET, UPSC, SSC, CGL, PSC, and so on. Usually, a number remains missing in the series. To find the missing number in the series we need to work out the logic and find out the logical pattern it is following. The missing numbers might occur in the middle of the series or at the end of the series given in the number series questions. The logical pattern will be similar.

Addition Pattern

When the number series follows an additional pattern, the numbers go on like 1, 3, 6, 10, 15,… and the next number is missing, the number will be calculated by following this logic

1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, 10 + 5 = 15, so 15 + 6 will be 21

The pattern could be the addition of integers or even numbers or odd numbers in the number series. To find the missing number in the series we need to look into the logic of the numbers which are being added.

For example, if the number series goes on with addition of consequential odd numbers like 1, 2, 5, 10, 17,… the series goes with following this logic 

1 + 1 = 2, 2 + 3 = 5, 5 + 5 = 10, 10 + 7 = 17, so the missing number in the series will be 17 + 9 = 26 

Subtraction Pattern

When the number series follows the logical reasoning of subtraction, then the missing number in the series can be found by subtracting the number which comes next in the calculation. 

For example, if the number series goes like 10, 8, 6, 4,… then the missing number could be found by subtracting 2 from the last number in the series

10 – 2 = 8, 8 – 2 = 6, 6 – 2 = 4, so the missing number will be 4 – 2 = 2

Square Pattern 

Sometimes, the number series proceeds with squares or cubes of the numbers. 

When the number series goes with the squares of the numbers like 1, 4, 9, 16, 25,…, 49, and the number series question is to find out the missing number, the number can be found by following the logic of square 

12  = 1, 22  = 4, 32  = 9, 42  = 16, 52  = 25, 72  = 49 then to find the missing number in the series, we need to find the square of 6, the next number will be 62  = 36

Cube Pattern

When the number series goes with cubic numbers, like 1, 8, 27, 64,… the next number could be found by doing cube of next the integer.

13 = 1, 23 = 8, 33 = 27, 43 = 64, so the missing number in the series will be 53 = 125

Combination Pattern

When the number series uses a combination of logical reasoning, then we need to find out the combination. Sometimes, there might be a combination of addition and multiplication, sometimes, the combination might be addition and square or addition and cube. Usually, addition remains constant.

When the number series question asks to find the missing number in this series, 1, 2, 6, 15,…, here it should be noted that the number series goes with the addition of the squares of the integers. So the next number can be found with the use of the same logical reasoning.

The series follows this logical pattern

1 + 11 = 2, 2+ 22 = 6, 6 + 32 =15, so the next number will be 15 + 42 = 31 

The series may also use cube of the integers.

For example, in the number series, 1, 10, 37,…, if the number series question asks to find out the missing number, then the cube of the next integer will be added to the last number

1 + 13  = 2, 2 + 23 = 10, 10 + 33 = 37, so the next number in the number series will be 37 + 43 = 101

Conclusion

The number series questions are easy to solve once you get the hang of the problems. We have discussed how to identify the logical pattern which is followed in the sequence and how to find the missing numbers in the series. There might be other types of questions included or merged with number series questions. For example, missing alphabets or missing words might also be merged in the number series questions. To learn more about those, alphabet series should be studied. There might be other patterns of number series questions, like the use of fractions and the use of negative numbers.