Sequences
Chapter Name : Sequences And Series |
Sub Topic Code : 104_11_09_02_01 |
Topic Name : Sequences |
|
Sub Topic Name : Sequences |
|
Introduction
Everything in this world that follows a pattern is a sequence. Prime numbers for example is a sequence.
Pre-Requisites:
Idea about numbers and progressions.
Activity:
Assuming a generation gap of 30 years, find the number of ancestors i.e. parents, grandparents, great grandparents, etc. over a span of 300 years.
Real Life Question:
How do we determine any term of Fibonacci series?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Sequence | A sequence can be regarded as a function whose domain is the set of natural numbers or a subset of it. |
| Finite sequence | A sequence containing finite number of terms. |
| Infinite Sequence | A sequence containing infinite number of terms. |
| nth term of the Sequence | The nth term is the number at the nth number in the sequence. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Calculator | Construct a sequence of numbers whose first term is 1 and second term is 1 and every consecutive term is sum of previous two terms. |
Real life uses :
Sequences have been used in the trading algorithms, applications and strategies. To model spiral of waves, breeding of animals and branching of tees etc.
Places to visit :
Math Lab.
Practical examples around us
| Examples | Explainations |
|---|---|
| 1. Fibonacci Sequence | 1, 1, 2,3,5,8… First two terms are ‘1’ and every next term is the sum of preceding two numbers. |
| 2. Prime Numbers | 2, 3,5,7,9… The prime numbers is a sequence of numbers having a special property. |
What you learn in Theory:
What is a sequence, infinite and finite sequence?
What you learn in Practice:
How to find a sequence and how to write a sequence.