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.
Have you counted? - like and share
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,
a 1 – first term of sequence
r – difference of sequence
• 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 a 1 and the difference r, we can find each term:
a n = a n-1 + r lub a n = a 1 + (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 first terms of an arithmetic sequence with the difference r is given by the formula: n = a 1 + a 2 + a 3 +... + a n
n = ((a 1 + a n)/2)ּn for S n = ((2a 1 + (n-1)r)/2)ּn