Geometric Progression
Chapter Name : Sequences And Series |
Sub Topic Code : 104_11_09_05_02 |
Topic Name : Geometric Progression |
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Sub Topic Name : General Term Of A G.P |
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Introduction
The common ratio of a geometric series may be negative, resulting in an alternating sequence, with numbers switching from positive to negative and back. For instance 1, ?3, 9, ?27, 81, ?243 ...is a geometric sequence with common ratio ?3.
Pre-Requisites:
Idea about sequences and series, geometric series.
Activity:
You drop a rubble ball from a height of 1 meter and it bounces back to lower and lower heights. Every time ball rises to 80% of its previous height. What height the ball will reach after the fifth bounce?
Real Life Question:
Emily’s salary for the current year is $15000. Every year her salary gets doubled. What will be her salary in 7th year?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Nth term of a GP | Let a GP with first non-zero term ‘a’ and common ratio r. Then nth term of the GP is given by: a_n= ?ar?^(n-1) |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Calculator | Write a number and multiply it consecutively with a constant number and write down the sequence obtained! |
Real life uses :
To model motion problems involving constant acceleration or deceleration. To model real life quantities such as monthly bills for cellular telephone services. To model nuclear fission reactions.
Places to visit :
Math Lab.
Practical examples around us
| Examples | Explainations |
|---|---|
| 1. Amoeba Multiplication | The reproduction process of amoeba forms a geometric series. |
| 2. Nuclear Fission | Each atoms cell splits into two atoms forming a GP. |
What you learn in Theory:
What are geometric arithmetic progressions and what is the nth term of the geometric series.
What you learn in Practice:
How the terms of geometric series are calculated.