# How to solve Number Series Questions | SSC, IBPS & DSSSB etc.

Number series tests present numerical sequences that follow a logical rule based on elementary arithmetic. An initial sequence is presented from which the rule must be deduced. Students are then asked to predict the next number that obeys the rule. They are required to find the correct way in which the series is formed and find out the missing number to complete the series.

## Some possible patterns of number series are:

### Prime Number Series

Prime numbers are numbers that are only divisible only by 1 and the number itself. (e.g. 2, 3, 5, 7, 11). A series of prime numbers is referred to as a prime number series.

Example of prime number series is: 5, 7, 13, 23 , ___ or 3, 5, 7, 11, 13, 17, ___

### MultiplicationSeries

When any series of numbers increases or decreases in multiples of a number, then that series is called multiplication series

Example of multiplication series is: 2, 4, 6, 8, ___ or 4, 12, 36, 108, ___ , 972

### Division Series

When any series on dividing the number with any digit gives the next number of the series then that series is called division series.

Example of division series is: 5040, 720, 120, 24, ___ , 2, 1.

Here, ^{5040}⁄_{7} = 720, ^{720}⁄_{6} = 120, ^{120}⁄_{5} = 24 and so on.

### Difference Series

A number series in which the difference between the numbers remains constant is called a difference series.

Example of difference series is 2, 6, 10, 14, 18,___, 26. Here, the difference in the series is 4 throughout the series. i.e. 6 - 2 = 4, 10 - 6 = 4, 14 - 10 = 4 and so on.

### n^{2} Series

A series in which the numbers are increasing in the n^{2} order, where n can be any number in a given order i.e. each number in the series will be the square of a number increasing or decreasing in a certain order.

Example:

n^{2} series is : 1, 9, 25, 49, 81, ___ , 169 the series is square of consecutive odd numbers. 1^{2}, 3^{2}, 5^{2}, 7^{2}, 9^{2} and so on.

### n^{2} + 1 Series

A series in which the numbers are in the sequence of n^{2} +1, where n can be any number in a given order.

Example:

(n^{2} + 1) series for positive integers starting at n = 2 is : 5, 10, 17, 26, 37, ___ , 65. The series is 2^{2} + 1, 3^{2} + 1, 4^{2} + 1, etc.

### n^{2} - 1 Series

A series in which the numbers are in the sequence of n^{2} - 1, where n can be any number in a given order.

Example:

(n^{2} - 1) series for decreasing positive integers starting at n = 10 is : 99, 80, 63, ___ , 35 . The series is 10^{2} - 1, 9^{2} - 1, 8^{2} - 1, etc. As you can see that here ānā is different for each number given in the series.

### n^{2} + n Series

A series in which the numbers are in the sequence of n^{2} + n, where n can be any number in a given order.

Example:

(n^{2} + n) series for increasing positive integers starting at n = 3 is : 12, 20, 30, 42, ___ . The series will be 3^{2} + 3, 4^{2} + 4, 5^{2} + 5, 6^{2} + 6 , etc. The next number will be 7^{2} + 7 which is 56.

### n^{2} - n Series

A series in which the numbers are in the sequence of n^{2} - n, where n can be any number in a given order.

Example:

(n^{2} -n) series for increasing positive integers starting at n = 1 is : 0, 2, 6, 12, 20, ___, 42 . The series will be 1^{2} - 1, 2^{2} - 2, 3^{2} - 3, 4^{2} - 4, 5^{2} - 5 , etc. The next number will be 6^{2} - 6 which is 30.

### n^{3} Series

A series in which the numbers are in the sequence of n^{3}, where n can be any number in a given order.

For example:

(n^{3}) series for increasing positive integers starting at n = 10 is : 1000, 8000, 27000, 64000, _____ . The series will be 10^{3}, 20^{3}, 30^{3}, 40^{3}, etc. The next number will be 50^{3} which is 125000.

### n^{3} + 1 Series

A series in which the numbers are in the sequence of n^{3} + 1, where n can be any number in a given order.

For example:

(n^{3} + 1) series for increasing positive integers starting at n = 1 is : 2, 9, 28, 65, ___, 217 . The series will be 1^{3} + 1, 2^{3} + 1, 3^{3} + 1, 4^{3} + 1, etc. The next number will be 5^{3} + 1 which is 126.

### n^{3} - 1 Series

A series in which the numbers are in the sequence of n^{3} - 1, where n can be any number in a given order.

For example:

(n^{3} - 1) series for increasing positive integers starting at n = 3 is : 26, 63, 124, ___. The series will be 3^{3} - 1, 4^{3} -1, 5^{3} - 1,etc. The next number will be 6^{3} - 1 which is 215.

### n^{3} + n Series

A series in which the numbers are in the sequence of n^{3} + n, where n can be any number in a given order.

For example:

(n^{3} + n) series for increasing positive integers starting at n = 4 is : 68, 130, 222, 350, ___, 738 . The series will be 4^{3} + 4, 5^{3} + 5, 6^{3} + 6, 7^{3} + 7, etc. The next number will be 8^{3} + 8 which is 520.

### n^{3} - n Series

A series in which the numbers are in the sequence of n^{3} - n, where n can be any number in a given order.

For example:

(n^{3} - n) series for increasing positive integers starting at n = 3 is : 24, 60, 120, 210, ___, 504 . The series will be 3^{3} - 3, 4^{3} - 4, 5^{3} - 5, 6^{3} - 6, etc. The next number will be 7^{3} - 7 which is 336.

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