Choose language

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

Have you counted? - like and share

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

Users of this calculator also used

Rail Fence, Zig-Zag - encoder / decoder

Rail Fence, Zig-Zag cipher online encoder and decoder. Encrypt and decrypt any cipher created in a Rail Fence, Zig-Zag cipher.

Quartiles Q1, Q2, Q3 of the interval series

With this statistical calculator, you will learn how to calculate the lower quartile, middle quartile, and upper quartile of an interval resolution series.

Addition in columns

With this calculator you will learn how to add in columns. You can check if the addition you have made is correct

Leverage, Operating Leverage, Total Leverage, Gearing

The DFL Finacial Leverage Calculator will help us calculate how sensitive the cash flow is to changes in operating profit.
With the DOL Operating Leverage Calculator, we will calculate how sensitive operating revenues are to changes in sales. The DTL Total Leverage Calculator will help us calculate the profit sensitivity to sales growth.

Online calculator

M+

M-

log

10^x

asin

acos

atan

e^x

sin^-1

cos^-1

tan^-1

sin

cos

tan

√

x²

1/x

x^M

(

)

exp

M+

M-

sin