Sum Of First N Terms Of An A P
Chapter Name : Arithmetic Progressions |
Sub Topic Code : 104_10_05_04_01 |
Topic Name : Sum Of First N Terms Of An A P |
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Sub Topic Name : Sum Of First N Terms Of An A P |
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Introduction
An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. This topic teaches you to find the sum of the arithmetic progression.
Pre-Requisites:
Idea arithmetic progressions, nth term of an AP.
Activity:
The number of gifts sent in the popular Christmas Carol “12 days of Christmas” forms a sequence. A part of the song goes this way “On the 12th day of Christmas my true love gave to me 12 drummers drumming, 11 pipers piping, 10 lords a leaping, 9 ladies dancing, 8 maids a milking, 7 swans a swimming, 6 geese a laying, 5 golden rings, 4 calling birds, 3 French hens, 2 turtle doves and a partridge in a pear tree.” How many gifts were given by the true love on the 12th day of Christmas?
Real Life Question:
Anna put $100 into her daughter’s money box when she was one year old, $150 on her second birthday, $200 on her third birthday and will continue in the same way. How much money will be collected in the money box by the time her daughter is 21 years old?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Sum of n terms of an AP | The sum of n terms of an AP is defined as the summation of all the n terms of the series. It is given by: S= n/2 [ 2a+(n-1)d ] |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Calculator | Enter the first term a, add the common difference d to find next term, add both the terms to find some up to two terms and so on. |
Real life uses :
Arithmetic progression are used in mathematical designs and patterns and also used in all engineering projects involving designs.
Places to visit :
Staircase.
Practical examples around us
| Examples | Explainations |
|---|---|
| 1. Staircase | The stairs in our home are an example of AP. Every step’s height is one unit greater than the previous one. |
What you learn in Theory:
What is the sum of an arithmetic progression and how to find it?
What you learn in Practice:
How to apply sum of arithmetic progression to real life problems.