Arithmetic sequence calculator and problems solver

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

Known Term Index

Known Term Value

Common difference

First Known Term Index

First Known Term Value

Second Known Term Index

Second Known Term Value

Term to Find

Calculate

First Term of the Arithmetic Sequence

 

Common Difference

 

nth Term of the Sequence Formula

 

Unknown Term equals to

 

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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.