Arithmetic Sequence Calculator

An online arithmetic sequence calculator instantly calculates the arithmetic sequence, nth term, sum, and indices of the series. The tool shows step by step calculations for arithmetic series that is obtained by adding a constant number with 100% accuracy. Just enter the required inputs and get the nth term of the sequence.

What Is Arithmetic Sequence?

In mathematics:

“A specific set of numbers in which each coming number is the resultant of the sum of the previous term and the common difference is known as the arithmetic sequence”

Arithmetic Sequence Formula:

Our arithmetic sequence formula calculator uses the following formulas to determine the arithmetic sequence and series accordingly:

For Finding nth Term:

$$ n^{th} Term = a + \left(n-a\right) * d $$

For Finding Sum of Arithmetic Progression:

$$ S = \frac{n}{2} * [2a_{1} +  \left(n-a\right) * d $$

Where;

• d = Common Difference
• a_1 = First Term 

How To Calculate Arithmetic Sequence?

Let us resolve an example that will help you to calculate arithmetic sequences manually! For instant outputs, you may still use the arithmetic sequence calculator.

Example # 01:

Find the 32nd term of the following arithmetic sequence:

$$ 39, 35, 31, 27, 23, … $$

Solution:

As we have:

$$  a_{1} = 39 $$

$$ d = 35 - 39 = -4 $$$$ n = 32 $$

Now we have 

$$ n^{th} Term = a + \left(n-a\right) * d $$

$$ a_{32} = 39 + \left(31-1\right) * -4 $$

$$ a_{32} = 39 + 31 * -4 $$ 

$$ a_{32} = 39 + 124 $$

$$ a_{32} = 163 $$

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

Example # 02:

Calculate the sum of up to 10 terms of the arithmetic sequence with the following attributes:

$$ a_{1} = 3 $$ 

$$ d = 2 $$ 

Solution:

Finding nth Term:

$$ n^{th} Term = a + \left(n-1\right) * d $$

$$ n^{th} Term = 3 + \left(10-1\right) * 2 $$

$$ n^{th} Term = 3 + \left(9\right) * 2 $$

$$ n^{th} Term = 3+18 $$

$$ n^{th} Term = 21 $$

Finding Sum up to 10 Terms:

$$ S = \frac{n}{2} * [2a_{1} +  \left(n-1\right) * d] $$

$$ S = \frac{10}{2} * [2 * 3 +  \left(10-1\right) * 2] $$

$$ S = \frac{10}{2} * [6 +  9 * 2] $$

$$ S = 5 * 6 +  9 * 2 $$

$$ S = 30 + 18 $$

$$ S = 48 $$

Writing Arithmetic Series:

Arithmetic Series = 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

Apart from the manual computations that could be tricky sometimes, you may better use this arithmetic calculator. The tool makes your task hassle-free and gets it done in moments with 100% accurate results.

How To Use Arithmetic Sequence Calculator?

This online arithmetic sequence solver is an extremely fast result-oriented tool. Keep scrolling to know how to use it!

Input:

• Enter the first term (a), common difference (d), and nth term number (n) in their respective fields
• Tap Calculate 

Output:

The arithmetic series calculator displays the following results within instants:

• Arithmetic sequence
• Nth term
• Sum from first to nth term

Faqs:

What Is The Difference Between Arithmetic Sequence and Series?

An arithmetic sequence is simply the set of objects created by adding a constant value each time. On the other hand, the arithmetic series is the sum of n objects in sequence. 

So the sum of the arithmetic sequence calculator finds that specific value that will be equal to the first value plus constant. The arithmetic series calculator helps to find out the sum of objects in a sequence.

How Do You Know If a Sequence Is Arithmetic or Geometric?

If it comes about the arithmetic sequence, then it is obtained by maintaining a constant difference between successive numbers and can be instantly determined by a common difference calculator. On the other hand, a geometric sequence has a constant ratio between numbers.

How Do I Find The Common Difference In an Arithmetic Sequence?

You can instantly figure out the common difference in an arithmetic sequence with this arithmetic sequences calculator. However, when it comes to manually, you can get the common difference by finding the difference between any two terms in an arithmetic sequence. 

References:

From the source of Wikipedia: Arithmetic progression, Product, Standard deviation