This Arithmetic Sequence Calculator calculates the n-th term and the sum of the first n terms of an arithmetic sequence, given the first term of the sequence and the common difference.
Arithmetic sequence formula
In mathematics, an arithmetic sequence, or arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant and is called the common difference. So, the formula for the \(n\)-th term is:
$${ a }_{ n } ={ a }_{ 1 } + d ⋅ (n – 1),$$
where \(d\) is the common difference.
The sum of the numbers in an arithmetic progression, also known as an arithmetic series, is expressed by the following formula:
$$n ⋅\frac { { a }_{ 1 } + { a }_{ n }}{ 2 }.$$
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