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A number series is an informal language of numbers. A number series is the sum of the terms of a sequence. Number series is a kind of series in which specific numbers are present in a specific order, and missing numbers need to be found. In today’s time, number series is an important part of every competitive examination. The number series can be of different types. Every type of number series requires its own tricks and formulas.
Types of number series
There are different kinds of number series based on different tricks as well as formulas. Given below are different kinds of number series :
Integer number series
The integer number series is the sequence of real numbers decimals as well as fractions. An example of integral number series is 2, 4, 6, 8, and so on.
Rational number series
Rational number series are those series that can be written as a quotient or fraction where both numerator and denominator consist of integers. An example of rational number series is 1/2, 1, 2, 4, and so on.
Arithmetic series
The arithmetic series is the mathematical series that consists of a series under which the next term generates by adding a constant to its previous number. An example of arithmetic series is 2, 7, 12, 17, 22, 27, in which the number 5 is added to its next number.
Geometric series
Geometric series is a series consisting of the multiplication of a constant number to every number. Examples of geometric series are 3, 6, 9, 12, 15, 18 and so on.
Square number series
Square number series is a sequence in which perfect squares of numbers are constructed. Examples of square number series are 1, 4, 9, 16, 25, 36 and so on.
Cube number series
Cube number series is a sequence in which perfect cubes of numbers are constructed. Examples of cube number series are 1, 8, 27, 64, 125 and so on.
Number series problems with solutions
- Find which number is missing in the given series.
3, 5, 5, 19, 7, 41, 9, ?
The answer is 71.
Explanation :
First series : 3, 5, 7, 9
Second series : 5, 19, 41, ?
Differences in the Second series are 14, 22, 30 etc
The next term is 41+30, which is equal to 71.
- What should be filled in place of a question mark (?) in the given number series?
132, 156, ?, 210, 240, 272
The answer is 182.
Explanation :
The given series follows a logic that
11 × 12, 12 × 13, 13 × 14, 14 × 15, 15 × 16,…
Therefore, the missing number is 13 × 14 = 182
- Find the missing number in the mentioned number series.
625, 625, 600, ?, 475, 875
The answer is 700.
Explanation :
The given number series 625, 625, 600, ?, 475, 875 follows a pattern :
625 + (0 x 0) = 625
625 – (5 x 5) = 625 – 25 = 600
600 + (10 x 10) = 600 + 100 = 700
700 – (15 x 15) = 700 – 225 = 475
475 + (20 x 20) = 475 + 400 = 875
Thus, the missing number in the given number series is 700.
- Find the missing number in the given series :
7, 8, 18, 57, ?, 1165, 6996
The answer is 232.
Explanation :
Here 2nd number = (1st number × 1 )+1
3rd number = (2nd number × 2 +2)
4th number = (3rd number × 3 )+3 and so on..
Thus, 5th number = (4th number × 4) +4 =57 × 4 + 4 =232.
- Find which number is wrong in the given series:
3, 8, 15, 24, 34, 48, 63
The answer is 34.
Explanation :
The difference between consecutive numbers is respectively 5, 7, 9, 11, 13 and 15.
Thus, 24 +11 = 35. However, it is given as 34 in the series. So, 34 is the wrong number.
Conclusion
The number series is a kind of series in which specific numbers are present in a specific order, and missing numbers need to be found. In today’s time, number series is an important part of every competitive examination. Number series are divided into different categories such as arithmetic series, geometric series, cube number series, square number series, quadratic series and special series.
The number series are generally based on either ascending or descending order of numbers. Each successive number is attained by multiplying or dividing the previous number by a particular number.
