Arithmetic Sequence Calculator

Arithmetic sequence calculator calculates the particular term of the arithmetic sequence and the total sum of all the sequence numbers, by the giving value of the first term and common difference.

What is Arithmetic Sequence

An arithmetic sequence is a sequence of numbers that has a common difference between the consecutive numbers.

For example,
if there is a sequence of numbers: 5, 12, 19, 26, 33
we need to check to see if there is a common difference. since
12-5=7
9-12=7
26-19=7
33-26=7
There is a common difference of 7, then it is an arithmetic sequence.

Arithmetic Sequence Formula

a_n = a₁ + d × (n-1)

while
a_n = last number of the sequence
a₁ = first number of the sequence
d = the difference between each consecutive sequence
n = the number of terms.

The sum of all of the numbers is:
a₁+a₂...+a_n

by calculating, it equals:
n x (a₁+a_n)/2

For example, if there is a total of 12 arithmetic sequence numbers, the first number of the sequence is 8, and the last number of the sequence is 107.

The sum of all of the numbers is calculated as:
n x (a₁+a_n)/2
=12 x(8+107)2
=6 x 115
=690.