# Sequence Calculator

The word sequence is used to describe the order of things. In case of the mathematics, sequence is considered to be a collection of objects which can be same or different where order does matter and repetition is also allowed. Just like a set – member of sequence are also known as terms and elements. Length of the sequence defines the number of the sequence. The difference between set and sequence is the repetition of the element, in case of set repetition is not allowed while in case of sequence it definitely is! A sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first n natural numbers (for a sequence of finite length n). Element position in a sequence is known as an index or a rank which is the natural number imaging the element. Whenever a symbol is used as a denotion to a sequence – the nth element of the sequence is showed by the n subscript such as Fn. Depending on the length, sequences can be finite (with limited element) or infinite (with unlimited elements).

## Types Of Sequence

Sequence is a huge topic and it is subdivided into different arena but there are four common types of sequence which are described below.

1. #### Arithmetic Sequences

An athematic sequence is a sequence in which each term is obtained by adding or subtracting a definite to the preceding number. It is the difference of two successive numbers. 2, 4, 6, 8, 10 is an arithmetic sequence with the common difference 2. If the first term of an arithmetic sequence is a1 and the common difference is d, then the nth term of the sequence is given by:

an=a1+(n−1)d

The sum of the sequence is called athematic series.

2. #### Geometric Sequences

In geometric sequences – each term is obtained by dividing or multiplying with a definite number with the successive number. Geometric sequence is shown as {a, ar, ar2, ar3, … } and the sum of the sequence is known as geometric series.

3. #### Harmonic Sequences

It is obtained by taking the reciprocals of an arithmetic progression. If the reciprocals can form an arithmetic sequence, it is will be known as harmonic sequence. Harmonic progression is another term used to describe harmonic sequence. This type of sequence is shown as 1/a1, 1/a2, 1/a3, and so on.

4. #### Fibonacci Numbers

Fibonacci numbers are known to form a sequence which can be obtained by adding two preceding elements. Sequence is defined as, F0 = 0 can and F1 = 1 and Fn = Fn-1 + Fn-2. Leonardo Fibonacci found the sequence of Fibonacci number and the sequence being with 1 and 1, the next number is 2 (1+1), the next number is 3 (1+2), and the next is 5 (2+3) and the list goes on. This sequence makes a visually appealing curve also known as Fibonacci spiral which is visible in nature whether you are counting the flower petal, checking the pine cone, following the shape of the hurricane, or shells.

## Application Of Sequence

Calculating the sequence can be useful in different scenarios such as to identify the portion of monthly payment to pay off a home or automobile loan. It can also help us list down the maximum temperature of the day in different areas throughout the year.

The practical implementation of sequence are not limited to only field of mathematics – they are diversely distributed. Sequence plays a vital role in the field of topology to study the metric spaces. It is also used in analysis to analyze the pattern of a phenomena. The practical use of sequence is also evident in linear and abstract algebra where several types of sequence are implied such as group and rings. Sequences are frequently utilized in the field of computer science where finite sequence are known as lists and infinite sequences are known as streams.

One of the most common use of sequence which can be observed in daily life is computing. Sequences are the main logical structure of algorithms or programs. When creating algorithms or programs, the instructions are presented in a specific correct order. A sequence can contain any number of instructions but each instruction must be run in the order they are presented. No instruction can be skipped. Algorithms provide the base for the computer system and operations as we know them today. Each and every computer programs we are using todays can be broken into three components and these components serve as the basis of computer programming. So what are these famous components? The answer is sequence, loops, and selection. Without sequence we cannot design, produce or run any program so no computer and definitely no internet!

Sequence calculator can help you solve all your sequencing problems. It is designed to cater to the requirements of all types of sequence such as geometric, harmonic, arithmetic, and Fibonacci. If you are worried about the calculating the amount you are supposed to pay each month to pay off a loan, you can use arithmetic calculator and it will not let you down. In rare case you come across with a product which is specifically designed to cater to your needs. When you operate the sequence calculator, you will be amazed by the precision, user ease, and operation of the calculator. As we have to solve the sequence almost each day and it was getting tiring to manually perfume all the calculations, we decided to make our life easy. We designed the calculator and used it for a year. Rather than investing hours we were performing our calculation in mere seconds and the process was so smooth that we have to share it with the world.

One of the best combo is that the manufacturers are also the user of the product and in this case – we were. So enjoy our effort to ease the process of calculating the sequence and let us know what you think about it!