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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 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.

PLANETCALC, Arithmetic sequence calculator and problems solver

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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Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Arithmetic sequence calculator and problems solver

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