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 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 2^{nd} term from the 1^{st} term.

The nth term in this series is denoted as T_{n} = 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 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, ar^{2}, ar^{3} …

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

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

The nth term of a G.P. series is denoted by T_{n} = ar^{n-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

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.

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.

This is a series consisting of prime numbers.

Example 2, 3, 5, 7, 11 …

This is a series consisting of square of numbers. The terms of this series is denoted as n^{2}.

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

This is a series consisting of cube of numbers. The terms of this series is denoted as n^{3}.

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

This is a series that follows the given rules

T_{0} = 1 and T_{1} = 1

T_{n} = T_{n-1 }+ T_{n-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.

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

Example 2, 5, 10, 17, 26 … is a n^{2}+1 series of natural numbers.

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

Example 2, 9, 28, 65, 126 … is a n^{3}+1 series of natural numbers.

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

Example 0, 3, 8, 15, 24 … is a n^{2}-1 series of natural numbers.

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

Example 0, 7, 26, 63, 124 … is a n^{3}-1 series of natural numbers.