SEQUENCES

Definition Let S be any non empty set .A function whose domain is the set N of natural number and whose range is a subset of S , is called sequence in the set S.

In other words a sequence in a set S is a rules which assigns to each natural number is a unique element of S.

A sequence whose range is a subset of R is called a real sequence or a sequence of real number .

A sequence can be described in several different ways.

1. Listing in order the first few element of a sequence till the rule for writing down different elements becomes clear .For example, <1,8,27,64,.....>is the sequence whose nth term is n^3.

2. Defining a sequence by the formula for its nth term .For example,the sequence <1,8,27,64,....> can also be written as <  1,8,.....,n^3,.....> or as<n^3:n belongs to N or simply as <n^3>.