### Sequences and Series

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**August 5th, 2011, 11:07 am**A sequence is a function whose domain is the set of natural numbers, N = {1, 2, 3, ...}. For the sequence 1, 4, 9, ..., whose terms are the squares of the natural numbers, it is common to use subscripts and write a[sub]1[/sub] = 1, a[sub]2[/sub] = 4, a[sub]3[/sub] = 9, ... instead of a(1) = 1, a(2) = 4, a(3) = 9, ..., as in other functions. The general or nth term for this function is a[sub]n[/sub] = n

If any term of a sequence is obtained by adding a constant to the preceding term, the sequence is called arithmetic. The terms of an arithmetic sequence there are:

^{2}If any term of a sequence is obtained by adding a constant to the preceding term, the sequence is called arithmetic. The terms of an arithmetic sequence there are:

- a[sub]1[/sub] = a

a[sub]2[/sub] = a + d

a[sub]3[/sub] = a + 2d

a[sub]4[/sub] = a + 3d

. . .

a[sub]n[/sub] = a + (n − 1)d