A sequence is a function whose domain is the set N of natural numbers.
Sequence is denoted by ‘a’ and the nth term in the sequence a(n) is denoted by an/sub>.
A sequence whose range is a subset of R is called a real sequence.
Representation of a sequence
One way is to list its first few terms till the rule for writing down other terms becomes clear.
Another way is to represent a real sequence is to give a rule of writing the nth term of the sequence.
If a1, a2, a3, … is a sequence, then the expression a1+a2+a3+… is a series.
It is not necessary that the terms of a sequence always follow a certain pattern or they are described by some explicit formula for the nth term. Those sequences whose terms follow certain patterns are called progressions.