INTRODUCTION
A number series is nothing but a sequence of numbers arranged in some logical way. This topic basically consists of a set of numbers connected by a specific pattern.Numbers can have interesting patterns. Here is the list of common patterns.
Types of number series:
Arithmetic Series
Geometric Series
Mixed Series
Exponential Series
Alternate Series
Special number Series
Arithmetic Series
ARITHMETIC SERIES
Arithmetic (Sum/Difference) Series: An arithmetic series is obtained by adding (or) subtracting the same value each time. These types of series will have a fixed difference between the two consecutive terms.EXAMPLE: 1, 4, 7, 10, 13, 16, …..
SOLUTION: The above sequence has a difference of 3 between each number.
The pattern is continued by adding 3 to the last number of each number.
Hence, the next term is 16 + 3 = 19
The value-added each time is called as “common difference”.
GEOMETRIC SERIES
Geometric (Multiplication/Division) Series: The pattern will be identified by multiplying or dividing the term by some number to obtain the next term.EXAMPLE: 1, 3, 9, 27, 81, …..
SOLUTION: Here the next term is obtained by multiplying by 3.
1 × 3 = 3
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
So, the next number should be 81 × 3 = 243.
GEOMETRIC SERIES
Geometric (Multiplication/Division) Series: The pattern will be identified by multiplying or dividing the term by some number to obtain the next term.EXAMPLE: 1, 3, 9, 27, 81, …..
SOLUTION: Here the next term is obtained by multiplying by 3.
1 × 3 = 3
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
So, the next number should be 81 × 3 = 243.
EXPONENTIAL SERIES
Exponential Series: These series will be in the form of ax. These series could be perfect squares or perfect cubes etc.EXAMPLE: 1, 4, 9, 16, 25, 36, 49, …..
SOLUTION: If you closely observe the given numbers, these are perfect square numbers.
Here, the pattern is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2
Hence, the next number becomes 8^2 = 64.
ALTERNATE SERIES
Alternate Series: In this for every alternate term forms a part of the series.EXAMPLE: 2, 4, 7, 14, 17, 34, 37, ?
SOLUTION: Here the pattern is alternate series as follows:
2 × 2 = 4
4 + 3 = 7
7 × 2 = 14
14 + 3 = 17
17 × 2 = 34
34 + 3 = 37
So, the next term is - 37 × 2 = 74
SPECIAL NUMBER SERIES
Prime numbers: Prime numbers are special numbers, which are divisible by only 1 and itself.Fibonacci series: Fibonacci series are special series where the present value is obtained by adding the previous two values.
Consider the series 1, 2, 3, 5, 8, 13, 21, …..
Here the logic is 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21
Hence, the next term is 13 + 21 = 34.
