# Number Series

Aptitude

Number series is an important chapter in an aptitude section. A number series is basically a sequence of numbers written in a certain order or pattern. And to solve these kinds of problems we have to find the pattern followed in the sequence.

Some of the most common series are discussed here.

## Arithmetic Progression (A.P.) Series

Arithmetic Progression or A.P. series are a sequence of numbers in which the difference between any two consecutive numbers is always the same.

A.P. series is of the form a, a+d, a+2d, a+3d …

Where, a is the first term and d is the common difference.

Common difference is calculated by subtracting the 2nd term from the 1st term.

The nth term in this series is denoted as Tn = a + (n-1)d

Set of even numbers is an example of A.P. series.

E = {2, 4, 6, 8, 10 …}

Here the first term a = 2 and the common difference d = 2.

## Geometric Progression (G.P.) Series

Geometric Progression or G.P. series are a sequence of numbers in the ratio of any two consecutive numbers is the same.

G.P. series is denoted as a, ar, ar2, ar3

Where, a is the first term and r is the common ration.

Common ration is calculated by dividing the 2nd term by the 1st term.

The nth term of a G.P. series is denoted by Tn = arn-1

X = {2, 4, 8, 16, 32, 64, 128, 256 …}

X is an example of G.P. series. The first term a = 2 and the common ratio r = 4/2 = 2

## Even number series

This is a series consisting of even numbers. This is also an example of A.P. series. The terms of this series is denoted as x, x+2, x+4, x+6 … where x is the first even number in the series.

Example 2, 4, 6, 8 … is an even number series.

## Odd number series

This is a series consisting of odd numbers. This is also an example of A.P. series. The terms of this series is denoted as x, x+2, x+4, x+6 … where x is the first odd number in the series.

Example 1, 3, 5, 7 … is an odd number series.

## Prime number series

This is a series consisting of prime numbers.

Example 2, 3, 5, 7, 11 …

## Square series

This is a series consisting of square of numbers. The terms of this series is denoted as n2.

Example 1, 4, 9, 16, 25 … is a square series consisting of the square of the natural numbers.

## Cube series

This is a series consisting of cube of numbers. The terms of this series is denoted as n3.

Example 1, 8, 27, 64, 125 … is a cube series consisting of the cube of the natural numbers.

## Fibonacci series

This is a series that follows the given rules

T0 = 1 and T1 = 1

Tn = Tn-1 + Tn-2 for all values of n >= 2

The first and second term is taken as 1 while any other term is equal to the sum of two previous terms.

Example 1, 1, 2, 3, 5, 8, 13, 21 … is a fibonacci series.

## n2+1 series

This is a series consisting of squares plus 1 of numbers.

Example 2, 5, 10, 17, 26 … is a n2+1 series of natural numbers.

## n3+1 series

This is a series consisting of cube plus 1 of numbers.

Example 2, 9, 28, 65, 126 … is a n3+1 series of natural numbers.

## n2-1 series

This is a series consisting of squares minus 1 of numbers.

Example 0, 3, 8, 15, 24 … is a n2-1 series of natural numbers.

## n3-1 series

This is a series consisting of cube minus 1 of numbers.

Example 0, 7, 26, 63, 124 … is a n3-1 series of natural numbers.