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Sequences and Series - Definitions

**Sequence**

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 a_{n/sub>.A sequence whose range is a subset of R is called a real sequence.Representation of a sequenceOne 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.SeriesIf a1, a2, a3, … is a sequence, then the expression a1+a2+a3+… is a series.ProgressionsIt 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.
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