Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: 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 .

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:

(i)

(ii)

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.

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