**Sequences Calculator:** Trying to figure out Sequences and looking for a online tool that makes your job easy. Learning will be much easier and fun with the Online Calculator for Sequence. Make the most out of the free online tools and get accurate yet straightforward descriptions. Understand the concept easily with the detailed procedure listed for Sequences.

If you are in search of a reliable tool for all your calculations related to Sequences. This is the best place and you will get various calculators for Sequences like Arithmetic, Geometric, etc. In order to meet your demands, we try to add calculators regarding the concept Sequence every day. Choose the one as per your need from the below available links.

- Fibonacci Calculator
- Sum of linear number sequence Calculator

A sequence is an ordered list of numbers. The numbers in the list are the terms of the sequence. A series is the addition of all the terms of a sequence. Sequence and series are similar to sets but the difference between them is in a sequence, individual terms can occur repeatedly in various positions. The length of a sequence is equal to the number of terms, which can be either finite or infinite. Let us start learning Sequence and series formula.

**What are Sequence and Series?**

A sequence is an ordered list of numbers. The numbers in the list are the terms of the sequence. The terms of a sequence usually name as *a _{i }*or

A series termed as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.

S_{N} = a_{1}+a_{2}+a_{3} + .. + a_{n}

**Sequences:** A finite sequence stops at the end of the list of numbers like a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}……a_{n. }whereas, an infinite sequence is never-ending i.e. a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}……a_{n….}.

**Series: **In a finite series, a finite number of terms are written like a_{1 }+ a_{2 }+ a_{3} + a_{4 }+ a_{5} + a_{6 + }……a_{n}. In case of an infinite series, the number of elements are not finite i.e. a_{1 }+ a_{2 }+ a_{3} + a_{4 }+ a_{5} + a_{6 + }……a_{n }+_{…..}

**Arithmetic Sequences:**

A sequence in which every term is obtained by adding or subtraction a definite number to the preceding number is an arithmetic sequence.

**Geometric Sequences:**

A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.

**Harmonic Sequences:**

If the reciprocals of all the elements of the sequence form an arithmetic sequence then the series of numbers is said to be in a harmonic sequence.

**Fibonacci Numbers:**

Fibonacci numbers form a sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F_{0} = 0 and F_{1} = 1 and F_{n} = F_{n-1} + F_{n-2}

The sequence of A.P: The n^{th} term a_{n} of the Arithmetic Progression (A.P) a, a+d, a+2d,…a, a+d, a+2d,… is given by

a_{n}=a+(n–1)d

Where,

a | First-term |

d | Common difference |

n | Position of the term |

l | Last term |

Arithmetic Mean: The arithmetic mean between a and b is given by **A.M=\(\frac{a+b}{2}\)**

The sequence of G.P: The nth term a_{n} of the geometric progression a, ar, ar^{2}, ar^{3},…, is **a _{n}=ar^{n}–1an=ar^{n–1}**

The geometric mean between a and b is **G.M= ±√ab **

Sequence of H.P: The n^{th} term a_{n} of the harmonic progression is **a _{n}= \( \frac{1}{a+(n–1)d} \)**

The harmonic mean between a and b is **H.M=\(\frac{2ab}{a+b}\)**

Series of A.P: If S_{n} denotes the sum up to n terms of A.P. a, a+d, a+2d,…a, a+d, a+2d,… then

S_{n} = \(\frac{n}{2}(a+l),\)

S_{n} = \( \frac{n}{2} [2a+(n–1)d] \)

The sum of n A.M between a and b is **A.M = \(\frac{n(a+b)}{2}\)**

Series of G.P: If S_{n} denotes the sum up to n terms of G.P is **S _{n}=\(\frac{a(1–rn)}{1–r}\); r≠1 and l=ar^{n}**

The sum S of infinite geometric series is **S=\(\frac{a}{1–r}; \)**

Solution: Given sequence is, 1, 3, 5, 7, 9……

- a) common difference d = 3 – 1 = 2
- b) The nth term of the arithmetic sequence is denoted by the term T
_{n}and is given by T_{n}= a + (n-1) d, - c) 21
^{st}term as: T_{21}= 1 + (21-1)2 = 1+40 = 41.

**1. What is the Sequence?**

The sequence is defined as the ordered list of numbers. Each number in the sequence is referred to as the term.

**2. What are some common types of Sequences?**

Some of the common types of Sequences include Arithmetic Sequence, Geometric Sequence, Harmonic Sequence, Fibonacci Series.

**3. How to use the Sequence Calculator?**

Just enter the inputs in the respective input field and click on the Calculate Button to know the output in the blink of an eye.

**4. Is there any Website that offers the best Sequence Calculator?**

Yes, Onlinecalculator.guru is a reliable and trustworthy site that provides the best Sequence Calculator. You can check out the online tools available for the concept sequence for guidance.