**Math Calculators** ▶ Arithmetic Sequence Calculator

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An online arithmetic sequence calculator that helps you to calculate the Arithmetic sequence, nth value, and sum of the arithmetic sequence. Read on to know about some basics related to arithmetic series, implementation of arithmetic sequence formula, and its working procedure.

An ordered list of numbers is known as a sequence whereas an Arithmetic Sequence is the series of numbers in which the difference between one term and the next term will be a constant. In simple words, we can say that we just have to add the same value every time. The existing difference among terms can either be positive or negative. An arithmetic series formula will help you out whenever you need to know any nth term in the arithmetic sequence.

Arithmetic sequence formula is: \(a^n=a^1+(n-1) d\)

- \(A^n\) = any nth term in the given sequence
- \(A^1\) = it represents the first term in the given sequenced = it is the common difference that exists among terms

An arithmetic sequence equation can be simplified and found by using this formula. Furthermore, an Online Harmonic Means Calculator allows you to calculate the harmonic mean from the dataset, by dividing the sum of reciprocals of the dataset.

**Example 1: **

You can make simpler calculations related to arithmetic sequence by using an arithmetic sequence calculator to find the nth term. However, a manual calculation can be as follows:

If the given sequence is “3, 8, 13, 18, 23, 28, 33, 38,….” then what will be the 9^{th} term?

- N = The difference among the numbers in the above sequence is 5
- D = first term is 3

We will apply the arithmetic sum formula to further proceed with the calculations:

$$ Xn = a + d(n−1) = 3 + 5(n−1) $$

$$ 3 + 5n − 5 $$

$$ 5n − 2 $$

So the next term in the above sequence will be:

$$ x9 = 5×9 − 2 $$

$$ 43 $$

**Example 2:**

To sum up the terms of the arithmetic sequence we need to apply the sum of the arithmetic formula. Therefore, if the term is1, 4, 7, 10, 13, … then by applying the formula we can find the unknown number.

- First term = 1
- The common difference = 3
- Terms to add up = 10

Therefore, by applying the sum of arithmetic sequence formula and putting values in it: So:

$$ Σ^{η – 1}_{k = 0}(α + kd) = n/2 (2a + (η – 1)d) $$

$$ Σ^{10 – 1}_{k = 0}(1 + k . 3) = 10/ 2 (2.1+(10 – 1).3) $$

On simplifying we will get: \( 5 (2 + 9·3) = 5 (29) = 145 \)

However, you can get these values by arithmetic sequence calculator directly just substitute the values in related fields.

A sequence can be defined as an arrangement of numbers in any specific order or a set of elements that follows a specific pattern. It may have a finite or infinite sequence. In contrast, a series can be defined as the sum of the elements of any given sequence in which the order of elements is not important. However, if the sequence is arithmetic then the sum of the arithmetic sequence can be taken by applying its formula.

While looking for a sum of an arithmetic sequence, it becomes essential to pick the value of “n” to calculate the partial sum. When you want to take the sum of all terms of the sequence then it will be the sum of infinite numbers. Instinctively, this sum of infinite numbers will be equal to infinity. Even if the common difference is positive, negative, or even equal to zero. The case might be different for different types of sequence for example in the case of a geometric sequence, the sum to infinity might be a finite term.

However, an Online Geometric Mean Calculator helps to calculate the geometric mean for a given data set of numbers or percentages.

An arithmetic series calculator can be used to calculate the sum and the nth number of sequence as follows:

- Enter the first number of the series and enter the common difference among the numbers.
- Enter the nth number which you want to obtain
- Hit to calculate button

- First of all, it displays an arithmetic sequence and the nth value.
- Then, the sum of arithmetic sequence from first to nth number.
- To make another calculation with this arithmetic sequence calculator just click the recalculate

The arithmetic series formula can be of two types that will represent two arithmetic equations:

- Recursive formulas
- Explicit formulas.

There are four basic and common types of sequence:

- Arithmetic Sequences that can be solved by implementing arithmetic sequence formula
- Geometric Sequences.
- Harmonic Sequences.
- Fibonacci Numbers.

Sequences, as well as Series, play a significant role in several aspects of our lives. By using them we can predict, assess and monitor the consequences of a situation or event. Sequence and series help us to make any decision.

A numerical pattern represents a sequence of numbers that have been generated based on a formula or a precise rule called a pattern rule. It can use one or more mathematical procedures to define the association among consecutive numbers in any pattern.

This arithmetic sequence calculator is an easily accessible option for analyzing a sequence of different values. Educators and students may take its support to find out the first term, nth term, and the sum of all numbers from first to nth terms in any of their calculations. It also eliminates the need to remember the arithmetic sequence formula that is needed in manual calculations. So you can rely on this calculator for quick, precise, and accurate calculations.

From the source of Wikipedia: Arithmetic progression, Derivation, Standard deviation, Intersections, Examples, and notation, Defining a sequence by recursion.

From the source of ChilliMath: Increasing and Decreasing Arithmetic Sequences, examples of Arithmetic Sequence.

From the source of Varsity Tutors: Arithmetic Sequences, nth term of an arithmetic sequence, common difference.