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# Arithmetic sequence calculator and problems solver

This online calculator solves common arithmetic sequences problems.

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 a its 5-th term equal to 12 and its 15-th term equal to 52. Find its 20-th term.

Some theory and description of the solutions can be found below the calculator.

#### Arithmetic sequence calculator and problems solver

First Term of the Arithmetic Sequence

Common Difference

nth Term of the Sequence Formula

Unknown Term equals to

### 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

$a_n=a_1+(n-1)d$

and in general

$a_n=a_m+(n-m)d$,

where d is the common difference.

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

$a_1=a_n-(n-1)d$

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

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

$d=\frac{a_n-a_m}{n-m}$

After that, it becomes the first type of problem.

For the convinience, the calculator above also calculates the first term and general formula for the n-th term of an arithmetic sequence.

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