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 separated by a fixed common difference....
A sequence in which the difference between any term and its predecessor is some constant. In particular, if a is the first term, then the ...
Sequence of numbers in which each term is produced by adding a constant term (the common difference d ) to the preceding one. It has the form ...