## Introduction to Arithmetic Sequence Calculator

**Common difference arithmetic sequence calculator** is an online solution for calculating difference constant & **arithmetic progression**. The common difference calculator takes the input values of sequence and difference and shows you the actual results.

Arithmetic sequence also has a relationship with arithmetic mean and significant figures, use math mean calculator to learn more about calculation of series of data.

## Formula used by Arithmetic Sequence Calculator

In order to know what formula arithmetic sequence formula calculator uses, we will understand the general form of an arithmetic sequence.

First term:

a_{1}

Second term:

a_{2}=a_{1} + d

Third term:

a_{3}=a_{1} + 2d

Fourth term:

a_{4}=a_{1} + 3d

Fifth term:

a_{5}=a_{1} + 4d

Arithmetic sequence formula for the nth term:

a_{n}=a_{1} + (n-1)

Here;

a_{n} = nth term

a_{1} = 1st term

n = term number

d = the common difference

If you know any of three values, you can be able to find the fourth.

Our sum of **arithmetic series calculator** will be helpful to find the arithmetic series by the following formula.

S = n/2 * (a_{1} + a)

By putting arithmetic sequence equation for the nth term,

S = n/2 * [a_{1} + a_{1} + (n-1)d]

And finally it will be:

S = n/2 * [2a_{1} + (n-1)d]

Now, this formula will provide help to find the sum of an arithmetic sequence. The factorial sequence concepts than arithmetic sequence formula.

## Difference between Arithmetic Sequence and Series

In this paragraph, we will learn about the difference between arithmetic sequence and series sequence, along with the working of sequence and series calculator.

Arithmetic sequence is simply the set of objects created by adding the constant value each time while arithmetic series is the sum of n objects in sequence. So the sum of arithmetic sequence calculator finds that specific value which will be equal to the first value plus constant. The arithmetic series calculator helps to find out the sum of objects of a sequence. Look at the following numbers.

Sequences | Series |
---|---|

Set of numbers with commas | Set of numbers with plus sign |

2, 4, 6, 8, 10, 12, 14, 16, 18… | 2 + 5 + 8 + 18 + 21 + 23 + 25 … |

9, 7, 0, -3, -6, -9, - 12, - 15, -18…. | |

40, 40.1, 40.2, 40.3, 40.4, 40.5… |

Arithmetic sequence is also called arithmetic progression while arithmetic series is considered partial sum.

## How to calculate Geometric Sequence?

Unlike arithmetic, in geometric sequence the ratio between consecutive terms remains constant while in arithmetic, consecutive terms varies. Arithmetic and geometric sequences calculator can be used to calculate geometric sequence online.

Example:

Determine the geometric sequence, if so, identify the common ratio

- 1, -6, 36, -216

Answer: Yes, it is a geometric sequence and the common ratio is 6.

- 2, 4, 6, 8

Answer: It is not a geometric sequence and there is no common ratio.

## What is Geometric Sequence formula?

The geometric sequence formula used by arithmetic sequence solver is as below:

a_{n} = a_{1} * rn−1

Here:

a_{n}= n^{th} term

a_{1 }=1^{st} term

n = number of the term

r = common ratio

## How to understand Arithmetic Sequence?

To understand an arithmetic sequence, let’s look at an example. Every day a television channel announces a question for a prize of $100. If anyone does not answer correctly till 4th call but the 5th one replies correctly, the amount of prize will be increased by $100 each day.

Suppose they make a list of prize amount for a week, Monday to Saturday. As the contest starts on Monday but at the very first day no one could answer correctly till the end of the week.

Monday | $100 |

Tuesday | $200 |

Wednesday | $300 |

Thursday | $400 |

Friday | $500 |

Saturday | $600 |

Here prize amount is making a sequence, which is specifically be called arithmetic sequence. To find the next element, we add equal amount of first. This is also one of the concepts arithmetic calculator takes into account while computing results.

## How to find Arithmetic Sequence Calculator?

You can **find the nth term of the arithmetic sequence calculator** to find the common difference of the arithmetic sequence. The approach of those arithmetic calculator may differ along with their UI but the concepts and the formula remains the same. You need to find out the best arithmetic sequence solver having good speed and accurate results.

## How to calculate Arithmetic Sequence?

The sum of arithmetic series calculator uses arithmetic sequence formula to compute accurate results. Below are some of the example which a sum of arithmetic sequence formula calculator uses.

### Example 1:

Given: 39, 35, 31, 27, 23….

#### Find : a_{32}

Solution:

a_{1}=39, d=−4, and n=32

a_{n}=a_{1} + (n−1)d

a_{32}=39 + (32−1)(-4)

85

For more detail and in depth learning regarding to the calculation of arithmetic sequence, find arithmetic sequence complete tutorial.

### Example 2:

a_{10} = 3.25

a_{12} = 4.25

#### Find : a_{1}

Solution:

a_{1} = 3.25

a_{3} = 4.25

n = 3

a_{n} = a_{1} + (n-1)

4.25 = 3.25 + (3-1)

d = 0.5

### Example 3:

Let us know how to determine first terms and common difference in arithmetic progression.

The third term in an arithmetic progression is 24

The tenth term is 3.

Find the first term and the common difference

Solution:

General formula for the nth term

a_{n} = a_{1} + (n-1)d

3rd term

equation 1 : 24 = a + 2d

10^{th} term:

equation 2 : 3 = a + 9d-

21 = -7d

So,

d = 21/-7 = -3

To find “a”, we will use equation 1

24 = a + 2d

24 = a + 2(-3)

24 = a + (-6)

So,

a = 24 + 6 = 30

So the first term is 30 and the common difference is -3.

2^{nd} part:

Now, find the sum of the 21^{st} to the 50^{th} term inclusive

There are different ways to solve this but one way is to use the fact of a given number of terms in an arithmetic progression is

1/3 n(a+l)

Here, “a” is the first term and “l” is the last term which you want to find and “n” is the number of terms. In this case first term which we want to find is 21st so

a_{21} = 30 + 20(−3) = −30

a_{50} = 30 + 49(−3) = −117

By putting values into the formula of arithmetic progression

1/2 n(a+l)

1/2 * 30 *(-30 + (-117))

= -2205

So -2205 is the sum of 21st to the 50th term inclusive.

## What is Calculatored's Arithmetic Sequence Calculator?

Calculatored has tons of online calculators and converters which can be useful for your learning or professional work. Our arithmetic sequence calculator with solution or **sum of arithmetic series calculator** is an online tool which helps you to solve arithmetic sequence or series. The arithmetic sequence solver uses arithmetic sequence formula to find sequence of any property.

Actually, the term “sequence” refers to a collection of objects which get in a specific order. Objects might be numbers or letters, etc. but they come in sequence. Objects are also called terms or elements of the sequence for which arithmetic sequence formula calculator is used.

## How to use Arithmetic Sequence Calculator?

Our **sum of arithmetic series calculator** is simple and easy to use. Just follow below steps to calculate arithmetic sequence and series using common difference calculator. The steps are:

Step #1: Enter the first term of the sequence (a)

Step #2: Enter the common difference (d)

Step #3: Enter the length of the sequence (n)

Step #4: Click "CALCULATE" button

Soon after clicking the button, our **arithmetic sequence solver** will show you the results as sum of first n terms and n-th term of the sequence. This way you can find the nth term of the arithmetic sequence calculator useful for your calculations.

Hope so this article was be helpful to understand the working of arithmetic calculator. If you find the common difference of the arithmetic sequence calculator helpful, please give us the review and feedback so we could further improve.