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Arithmetic sequence calculator

You can easily and quickly calculate the sum of an arithmetic sequence, calculate the value and the difference of an arithmetic sequence or find the nth expression.

To get the result, enter the appropriate data into the empty fields of the calculator.

Arithmetic sequence / Find n-th term

Enter a value

a₁

Enter the difference

Number of term you want to count the value:

a_n

sequence:

Arithmetic Sequence / Sum

Enter how many first terms of the above sequence you want to add:

Sum

Arithmetic Sequence / a₁ and r

Enter the number of term in the sequence:

Enter value:

Enter the number of the next term in the sequence:

Enter value:

a₁

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Useful information

Arithmetic sequence is a sequence in which each term (except the first) is formed by adding a fixed number r to the previous term. The difference of consecutive terms of the arithmetic sequence is constant, equal to r.
The number r is called the difference of the arithmetic sequence.

We call a sequence an arithmetic if for each n, a_n+1-a_n= r = constans,

. a₁ – first term of sequence
r – difference of sequence

If:
• r > 0 then the sequence is ascending
• r < 0 then the sequence is descending
• r = 0 then the sequence is constant

Given the first term of a₁ and the difference r, we can find each term:

a_n = a_n-1 + r lub a_n = a₁ + (n-1)r

Corelation between three consecutive terms in an arithmetic sequence:

a_n = (a_n-1 + a_n+1)/2 for n ≥ 2

The above formula shows that each term of the arithmetic sequence except the first (if the sequence is finite) and the last is the arithmetic mean of two adjacent terms (previous and next terms):

Sum S_n = a₁ + a₂ + a₃ +... + a_n , n first terms of an arithmetic sequence with the difference r is given by the formula:

S_n = ((a₁ + a_n)/2)ּn for S_n = ((2a₁ + (n-1)r)/2)ּn

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