Arithmetic sequences calculator

This online tool can help you find n^th term and the sum of the first n terms of an arithmetic progression. Also, this calculator can be used to solve much more complicated problems. For example, the calculator can find the common difference ($d$) if $a_5 = 19 $ and $S_7 = 105$. The biggest advantage of this calculator is that it will generate all the work with detailed explanation.

Basic calculator Solve for a₁ and d Solve for n

Arithmetic Sequences Calculator

Find n - th term and the sum of the first n terms.
help ↓↓ examples ↓↓ tutorial ↓↓

First term (a₁) :

Common difference (d) :

Number of Terms (n) :

Choose what to compute

a_n (the n-th term)

S_n (the sum of the first n terms )

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Arithmetic Sequences Calculator

Use this one if you need to find either a1 or d.
help ↓↓ examples ↓↓ tutorial ↓↓

Enter values in two out of four rows.

First term (a₁):

Common difference (d):

Enter n-th term

$a($ $)=~$

Sum of first n terms

$S($ $)=~$

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Arithmetic Sequences Calculator

This calc will find unknown number of terms.
help ↓↓ examples ↓↓ tutorial ↓↓

Enter values in three out of four rows.

First term (a₁) :

Common difference (d) :

Enter n-th term

$a~(~n~)~=~$

Sum of first n-terms

$S~(~n~)~=~$

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Get Widget Code

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Examples

ex 1:

1 + 2 + 3 + 4 + . . . + 98 + 99 + 100 = ?

ex 2:

The first term of an arithmetic sequence is equal to 5/2 and the common difference is equal to 2. Find the value of the 20^th term.

ex 3:

An arithmetic sequence has a common difference equal to 7 and its 8^th term is equal to 43. Find its first term.

ex 4:

Determine the first term and difference of an arithmetic progression if a₃ = 12 and the sum of first 6 terms is equal 42.

ex 5:

The first term of an arithmetic progression is -12, and the common difference is 3 determine how many terms must be added together to give a sum of 1104.

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About this calculator

Definition:

Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant. The constant is called the common difference (d).

Formulas:

The formula for finding $n^{th}$ term of an arithmetic progression is $\color{blue}{a_n = a_1 + (n-1) d}$, where $\color{blue}{a_1}$ is the first term and $\color{blue}{d}$ is the common difference.

The formulas for the sum of first $n$ numbers are $\color{blue}{S_n = \frac{n}{2} \left( 2a_1 + (n-1)d \right)}$ and $\color{blue}{S_n = \frac{n}{2} \left(a_1 + a_n \right)}$.

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