Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Introduction and types of Sequence

Introduction:

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.

Sequence -: 

A sequence is a function whose domain is  N .

Real Sequence -:

If the range of a sequence is a subset of  R, it is called a Real Sequence.

Complex Sequence -:

If the range of a sequence is a subset of  \mathbb{C} (complex number), it is called a Complex Sequence.

Terms of a Sequence -:

The functional values  f(n) of a sequence  f:N\to R 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 -:   f:N\to R such that:

(i)  f(n) = 2n+3

(ii)  f(n) = (-1)^{n+1}

are examples of Real Sequences.

A sequence  f is usually denoted in either of the forms  \left\{ t_n \right\}_{n=1}^\infty , or simply as  \{t_n\} or  (t_n) , where  f(n) = t_n .

 t_n is called the  n^{th} term of the sequence. Accordingly  t_1,\ t_2,\ t_3... are termed as  1\text{st}, 2\text{nd}, 3\text{rd}… terms of this sequence.

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