The phrase ‘one after another’ on a variety of occasions. The days in a week, the months and seasons in a year. Their occurrence one after another chains them in an order relation. This is logically named as a Sequence.
A sequence is a function whose domain is .
Real Sequence -:
If the range of a sequence is a subset of it is called a Real Sequence.
Complex Sequence -:
If the range of a sequence is a subset of (complex number), it is called a Complex Sequence.
Terms of a Sequence -:
The functional values of a sequence are called the Terms of the Sequence.
Finite and Infinite Sequences -:
A sequence with finite numbers of terms is called a finite sequence, otherwise, it is called an Infinite Sequence.
Ex -: such that:
are examples of Real Sequences.
A sequence is usually denoted in either of the forms , or simply as or , where .
is called the term of the sequence. Accordingly are termed as terms of this sequence.