# Arithmetic sequence calculator and problems solver

This online calculator solves common arithmetic sequences problems.

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#### Timur

Criado: 2019-07-06 02:59:18, Ultima atualização: 2021-02-12 11:03:59

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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

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 the first type of problems listed above by using the general formula directly or 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 problem, 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.

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

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