Evaluate the related series of each sequence calculator

This online calculator can solve arithmetic sequences problems. Currently, it can help you with the two common types of problems:

1. Find the n-th term of an arithmetic sequence given m-th term and the common difference. Example problem: An arithmetic sequence has a common difference equal to 10, and its 5-th term is equal to 52. Find its 15-th term.

2. Find the n-th term of an arithmetic sequence given i-th term and j-th term. Example problem: An arithmetic sequence has its 5-th term equal to 12 and its 15-th term equal to 52. Find its 20-th term.

Some formulas and descriptions of the solutions can be found below the calculator.

Arithmetic sequence calculator and problems solver

Problem type

Find term by another term and common difference

Find term by two another terms

First Term of the Arithmetic Sequence

nth Term of the Sequence Formula

Arithmetic sequence

To recall, an arithmetic sequence or arithmetic progression (AP) is a sequence of numbers such that the difference, named common difference, of two successive members of the sequence, is a constant.

Thus, the formula for the n-th term is

and in general

,

where d is the common difference.

You can solve the first type of problems listed above by using the general formula directly or calculating the first term a1, using the formula.

And then using the formula for the n-th term.

For the second type of problem, you need to find common difference using the following formula derived from the general formula.

After that, it becomes the first type of problem.

The calculator above also calculates the first term and general formula for the n-th term of an arithmetic sequence for convenience.

'Sum of Arithmetic Sequence Calculator' is an online tool that helps to calculate the sum of the arithmetic sequence. The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms.

What is the Sum of Arithmetic Sequence Calculator?

Online Sum of Arithmetic Sequence calculator helps you to calculate the sum of arithmetic sequence in a few seconds. An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.

Sum of Arithmetic Sequence Calculator

NOTE: Please enter first term, common difference upto four digits only and enter number of terms upto three digits only.

How to Use Sum of Arithmetic Sequence Calculator?

Please follow the steps below to find the sum of the arithmetic sequence:

• Step 1: Enter the first term(a), the common difference(d), and the number of terms(n) in the given input box.
• Step 2: Click on the "Calculate" button to find the sum of the arithmetic sequence.
• Step 3: Click on the "Reset" button to clear the fields and find the sum of the arithmetic sequence for different values.

How to Find Sum of Arithmetic Sequence?

An arithmetic sequence is defined as a series of numbers, in which each term (number) is obtained by adding a fixed number to its preceding term.

Sum of arithmetic terms = n/2[2a + (n - 1)d], where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.

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Solved Examples on Sum of Arithmetic Sequence Calculator

Example 1:

Find the sum of the arithmetic sequence 1,3,5,7,9,11,13,15

Solution:

Given: a = 1, d = 2, n = 8

Sum of arithmetic terms = n/2[2a + (n - 1)d]

= 8/2[2(1) + (8 - 1)2]

= 4[2 + 14]

= 64

Example 2:

Find the sum of the arithmetic sequence 2, 7, 12, 17, 22

Solution:

Given: a = 2, d = 5, n = 5

Sum of arithmetic terms = n/2[2a + (n - 1)d]

= 5/2[2(2) + (5 - 1)5]

= 5/2[4 + 20]

= 5 × 12

= 60

Example 3:

Find the sum of the arithmetic sequence for a = 10, d = 9, and n = 20

Solution:

Given: a = 10, d = 9, n = 20

Sum of arithmetic terms = n/2[2a + (n - 1)d]

= 20/2[2(10) + (20 - 1)9]

= 10[20 + 171]

= 1910

Similarly, you can try the sum of arithmetic sequence calculator to find the sum of the arithmetic sequence for the following: 

a)  2,4,6,8,10,12,14,15   b)  5,15,25,35,45,55,65

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• Arithmetic Sequence
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