Arithmetic sequence calculator

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