Geometric Progression
Chapter Name : Sequences And Series |
Sub Topic Code : 104_11_09_05_03 |
Topic Name : Geometric Progression |
|
Sub Topic Name : Sum To N Terms Of A G.P |
|
Introduction
Sum of a geometric progression involves finding the sum of all the n terms of the series.
Pre-Requisites:
Idea about sequences and series, geometric series.
Activity:
Take a square piece of paper and divide it into four equal parts. Now further divide the four equal parts into four equal parts and see the number of square pieces of paper obtained after each iteration. How many squares were formed in total?
Real Life Question:
What is the sum: 2+4+6+8+10+………………………………+220?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Sum of n terms of a GP | Let ‘a’ be the first non zero term of a GP and ‘r’ be its common ration then Sn, the sum of n terms is denoted by: Sn = a+ ar + ar2 + …………..+ arn-1 S_n= (?a(1-r?^n))/(1-r) or S_n= (?a(r?^n- 1))/(r-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! Find the sum of the sequence. |
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. Designing of fractals.
Places to visit :
Math Lab.
Practical examples around us
| Examples | Explainations |
|---|---|
| 1. Amoeba Multiplication | The reproduction process of amoeba forms a geometric series. |
| 1. Nuclear Fission | Each atoms cell splits into two atoms forming a GP. |
What you learn in Theory:
What is a geometric sequence and a geometric series?
What you learn in Practice:
How to find the sum of a geometric series and apply it to real world.