Quantitative Aptitude Concepts and Sample Questions Number Series and Sequences

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Number Series and Sequences is an important topic for any competitive exam. Types of questions in this topic includes

• Find the missing term or next term in given series
• Find the wrong term in given series

Number Series

A number series is a sequence of many numbers written from left to right in a certain pattern. They always follow some pattern or the specific rules; we just have to recognize the pattern or rule to solve the questions.

1. Prime Number Series

In these types of series, a series is made by using prime numbers and arranging them in different patterns.

Example 1.  Find out the next term in the series?

7, 11, 13, 17, 19,………………..

Solutions: Given series is a consecutive prime number series. Therefore, next term in series will be 23.

1. Multiple Series

In these types, series proceeds as a multiple of a specific numbers.

Example: Find out the missing term in the series 4, 8, 16, 32, 64, ……………256.

Solutions: Here, every next number is double the previous number.

Required number= 64 x 2 = 128

1. Division Series

As similar to Multiple series, the numbers in series are divided by some specific number.

Example: Find out the missing term in the series, 80, 200, 500, ?, 3125

Solutions: 80 x 5/2 = 200

200x 5/2 = 500

500 x 5/2 = 1250

1250 x 5/2 = 3125

Hence, missing term is 1250

Difference or Addition Series

In these types, the pattern followed is of adding or subtracting a specific number.

Example: Find out the missing term in the series 108, 99, 90, 81, ………………….63.

Solutions: Here, every next number is 9 less than the previous number.

Therefore, Required number = 81-9 = 72

n²  Series

The pattern followed in of adding or subtracting a specific number.

Example: find out the missing term in the series 4, 16, 36, 64,……………………….. 144.

Solution: This is a series of square of consecutive even numbers.

i.e 2² =4

4² = 16

6² = 36

8² = 64

10²= 100

12² = 144

Hence missing term is 100

(n²+1) Series

Here 1 is added to the square term to form the series.

Example: 10, 17, 26, 37, ……………………………65.

Solution: Series Pattern is

3² +1=10

4²+1 = 17

5²+1=26

6²+1= 37

7²+1= 50

8²+1= 65

Therefore, required number =50

(n²-1) Series

In this series 1 is subtracted from the square number like 1 was added (n2+1) series.

Example: find out the missing term in the series 0, 3, 8, 15, 24, ?, 48

Solution: Series Pattern is

12-1 = 0

22-1 = 3

32-1= 8

42-1=15

52-1=24

62-1=35

72-1= 48

Required number= 35

(n²+n) Series

In this series the same number is added to its square term to form series

Example: find out the missing term in the series 420,930, 1640, ………..3660.

Solution: Series pattern is 20²+20, 30²+30, 40²+40, 50²+50

Required number = 50²+50

Similar pattern will be applicable for n³ series