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What is Sequence & Series ? Basics of Sequence and SeriesItsMyAcademy.com

What is Sequence & Series ? Basics of Sequence and Series


In earlier classes , you might have come across various patterns of numbers like

1,       3,       5,      7,       9, …….

0,      -2,     -4,     -6,     -8, ………….

1,      4,        9,     16,     25………..

These patterns are generally known as sequences. Now in these sequence and series introductory video will learn what is exactly sequence and what is series, we will discuss.

Sequences

As we mentioned above, sequence can be think as a arrangement of numbers of which one number is designated as the first , another as the second , another as third and so on..is known as sequence.

Let’s consider an arrangement of numbers to understand the sequence more ..

1  ,          8  ,          27   ,         64 ,               125  

1   ,         ½  ,         1/3,           ¼  ,              1/5  

2  ,         4     ,         6 ,              8   ,              10 

In each of the above arrangements numbers are arranged in a definite order according to some rule.

In the first arrangement the numbers are cubes of natural numbers and in the second arrangement the numbers are reciprocals of natural numbers whereas in the third arrangement the numbers are even natural numbers.

Each of the above arrangement is a sequence. Thus we can now define the sequence

Definition of Sequence

A sequence is an arrangement of numbers in a definite order according to some rule.

After learning sequence , lets learn what is series, series is nothing more than the sum of the sequence.

If you represent the sequence by replacing its comma by + sign it is then called series.

Terms and Symbol to Denote

The various numbers occurring in a sequence or series are called its terms. We generally denote them by a1, a2, a3, … or  t1 , t2 , t3 ,….

In earlier classes , you might have come across various patterns of numbers like

1, 3, 5, 7, 9, …….

0, -2, -4, -6, -8, ………….

1, 4, 9, 16, 25

These patterns are generally known as sequences. Now in these sequence and series introductory video will learn what is exactly sequence and what is series, we will discuss.

Sequences

As we mentioned above, sequence can be think as a arrangement of numbers of which one number is designated as the first , another as the second , another as third and so on..is known as sequence.

Let’s consider an arrangement of numbers to understand the sequence more ..

1    8 27    64   125

1  ½    1/3 ¼  1/5

2   4   6   8   10

In each of the above arrangements numbers are arranged in a definite order according to some rule.

In the first arrangement the numbers are cubes of natural numbers and in the second arrangement the numbers are reciprocals of natural numbers whereas in the third arrangement the numbers are even natural numbers.

Each of the above arrangement is a sequence. Thus we can now define the sequence

Definition of Sequence

A sequence is an arrangement of numbers in a definite order according to some rule.

After learning sequence , lets learn what is series, series is nothing more than the sum of the sequence.

If you represent the sequence by replacing its comma by + sign it is then called series.

Terms and Symbol to Denote

The various numbers occurring in a sequence or series are called its terms. We generally denote them by a1, a2, a3, … or t1 , t2 , t3 ,….

a = first term of the sequence or series

An = nth term of the sequence

L = last tern of the sequence

Sn = sum of the n terms of the sequence etc …

a = first term of the sequence or series

An = nth term of the sequence

l = last tern of the sequence

Sn = sum of the n terms of the sequence etc …

Some other related links:

2. Finite Sequence & Infinite Sequences – Types of Sequences & Series

3.  How to Find the First Five (5) Terms of a Sequence ?

4. How to Find the Indicated Terms of Given Sequence ?

5.  Types of Sequences

Arithmetic Sequence  (Arithmetic Progression)

6.. Arithmetic Sequence (Arithmetic Progression) – Basics

7.  How to Check Arithmetic Sequences Situations 1

8. How to Confirm If They are Arithmetic Progression

9. How to Write the First Four (4) terms of an Arithmetic Sequences


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