Arithmetic Sequence Calculator

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An arithmetic sequence or series calculator is a tool for evaluating a sequence of numbers, which is generated each time by adding a constant value. It is also known as the recursive sequence calculator.

It gives you the complete table depicting each term in the sequence and how it is evaluated. You can also find the graphical representation of the sequence.

How to use the arithmetic series calculator?

Follow these steps to find the arithmetic series.

  1. Enter the nth term and its value in the first box.
  2. Enter the total number of terms and the total number of terms.
  3. Click "Calculate".

Moreover, you will get all the steps that are performed by this calculator to calculate the terms in the sequence and the sum of the sequence.

The n-th term is computed by: --
The first element of the sequence is: --

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In this post, we will discuss the arithmetic sequence, its formula, and examples. 

What is an arithmetic sequence?

A set of objects, including numbers or letters in a certain order, is known as a sequence in mathematics. The sequence's objects are known as terms or elements. It is quite normal to see the same object in one sequence many times.

Arithmetic sequence definition can be interpreted as:

                               "A set of objects that comprises numbers is an arithmetic sequence. A constant number known as the common difference is applied to the previous number to create each successive number."

The common difference refers to the difference between any two consecutive terms of the sequence.

Arithmetic sequence formula

We can use the arithmetic sequence formula to find any term in the sequence. Arithmetic sequence equation can be written as:

aa = 1+(n1)d1 + (n-1)d

In this equation:

ana_n refers to the nthn^{th} term of the sequence,

a1a_1 refers to the first term of the sequence,

dd refers to the common difference and

nn refers to the length of the sequence.

The above formula is an explicit formula for an arithmetic sequence. All terms are equal to each other if there is no common difference in the successive terms of a sequence. In this case, there would be no need for any calculations.

How to calculate arithmetic sequence?

Find the 10th term in the below sequence by using the arithmetic sequence formula.

2,4,6,8,10,12,14,16,18...2, 4, 6, 8, 10, 12, 14, 16, 18...

Solution:

As we know, n refers to the length of the sequence, and we have to find the 10th term in the sequence, which means the length of the sequence will be 10. Follow these steps to find a specific term in an arithmetic sequence.

Step 1: Write down the sequence.

2,4,6,8,10,12,14,16,18...2, 4, 6, 8, 10, 12, 14, 16, 18...

Step 2: Find the common difference d.

d=n2n1d = n_2 - n_1

d=2d = 2

Step 3: Write down the formula of the arithmetic sequence.

an=a1+(n1)da_n = a_1 + (n-1)d

Step 4: Substitute the values in the equation.

As we know,

a1=2,n=10,a_1= 2, n = 10, and d=2d = 2

a10=2+(101)2=20a_{10} = 2 + (10 - 1) 2 = 20

So the 10th term of this arithmetic sequence would be 20. You can also use our above arithmetic sequence formula calculator to find the required value.

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Isa W. Monsour | 19/08/2019

It’s a well-designed calculator for the students. You can also easily understand it.

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