Number Series

In the mathematical or statistical background the use of “Number series” can be seen. Other than that in the management aptitude tests the series can be used in the case of reasoning related mathematics. The value or the sequences can be solved by observing and finding similarities among the “series”. Not only the numeric but the alphabets are also used in the “series” and they are also arranged in a specific order. The topics of “reasoning” that can include the use of “number series” are “clocks”, “calendars”, “direction and distance”, “data sufficiency”, “coding and decoding” related mathematics in the general intelligence exams.

What is a “number series”?

The arrangement of numeric that can follow a similar trail can be defined as the “number series”. An individual should find the wrong patterns or the missing digit in the “series” and can thus complete the whole sequence. There are no such specific patterns in the example of mathematical reasoning. The key concept of the series has to be understood and the nature of the pattern can be cleared. In the case of the “Number series reasoning”, the Fibonacci sequence can also be found where the previous two numerics of the sequence are to be added to find the sequence. Other than that, the convergent series also can be included in the “number series” where there is a definite limit and linked with an infinite series. 

Properties of “number series”

The infinite series or the simple series can be called the infinite addition symbolised by a countenance where operators can take infinite arguments or numeric. On the other hand, in a convergent series, the series that denotes Σan, is likely to be convergent as sums have an absolute limit. The particular wrong number has to be denoted by visualising the given “number series”. Moreover, the missing number can also be included in the case of the reasoning with the series. The series can contain the sequence of perfect squares and can also contain the order of perfect cubes. On the other hand, the ascending or descending directive of the numbers can be found in this kind.To solve problems in particular cases, multiplication and division can be used.

Several sequences and formulas are used in the problems to solve them following a specific pattern. The nth term of the series can be solved by considering the first term and the common difference among the numbers. The sum of the n terms is equivalent to the multiple of n/2 and the addition of the first term of the arithmetic series. In the case of the geometric series, the nth term can be defined by finding the first term and the standard ratio. The power of the term r is 1 lesser than the number of terms in the geometric series.

Types of number series

There are several types of “Number series” and they are “addition series”, “multiplication series”, and “division series”,“ subtraction series. Other than that there are other types of series that include “arranging number”, “Fibonacci series”, “Square series”, “cube series”. Moreover, the important types of series that are often used in statistical and mathematical problems are “Altering series”, and “mixed operator series”.

• Division series: in this kind of “number series reasoning” the type of a particular number is divided so that the successive number can be achieved.
• Square series: in this type all the numbers are present are generally in a perfect square sequence arranged in a specific pattern
• Addition series: the numbers are added to definite numeric in order to get the next number
• Subtraction series: Like the addition series here the subtraction can be done from a definite number to get the subsequent number
• Cube series: each digit in the sequence are in the perfect cube form and the next number will be also in a perfect cube form
• Multiplication series: a specific type of numeric should be multiplied in order to get the next one
• Fibonacci series: the next number is the sum of the previous 2 numbers
• Mixed operator series: more than one operation has to be done to get the next digit in this kind of reasoning
• Alternating series: the patterns are used in an alternative form in the “number series”

Number series solved example

Question 1: Here is a series, 3, 6, 11,18,27,?, 51

3+3=6

6+5=11

11+7=18

18+9=27

27+11=38

38+13=51

Therefore the missing number is 38 and this is based on the addition series.

Question 2: 49, 121, 169, ?, 361

7^2=49

11^2=121

13^2=169

17^2=289

19^2=361

Therefore the right answer will be 289 and this has been done with the square series.

Conclusion

The study concludes the basic use of the number series and the types of the “number series” that are used in the reasoning and aptitude based questions. This is used to determine the missing or wrong number in a specific sequence and can be solved by understanding the underlying pattern of the given series. Different formulae are also used in order to determine and find the correct answer in the convergent and arithmetic or geometric series.