A sequence in which each term (except the first) differs from the previous one by a constant amount, the common difference. If the first term is a and the common difference is d, then the progression takes the form
a, a + d, a + 2d, a + 3d, …
and the nth term is
a + (n-1)d
A sum of the terms of such a progression is an arithmetic series:
a + (a + d) + (a + 2d) + ….
The sum of the first n terms is given by
na + 1/2n(n - 1)d
or alternatively by
1/2n[2a+(n - 1)d]
Compare geometric progression.
A sequence of numbers, called terms , such that any two consecutive numbers in the sequence are in a fixed common ratio. The geometric...
Sequence of numbers or terms that have a common difference between any one term and the next in the sequence. For example, 2, 7, 12, 17, 22, 27, ...
in mathematics, sequence of quantities, called terms, in which the relationship between consecutive terms is the same. An arithmetic progression is