Class 10 Exam > Class 10 Notes > Lab Manual: Arithmetic Progression II
Lab Manual: Arithmetic Progression II - Class 10 PDF Download
Objective
To verify that the sum of first n natural numbers is (n(n+1)/2) by graphical method.
The product of two polynomials say A and B represents a rectangle of sides A and B. Thus n(n+1) represents a rectangle of sides n and (n + 1).
Prerequisite Knowledge
- Concept of natural numbers.
- Area of squares and rectangles.
Materials Required
Graph papers, white chart paper, coloured pens, geometry box.
Procedure
Let us consider the sum of first n natural numbers 1 + 2 + 3 + 4 + + n (say n = 10).
- Take a graph paper and paste it on a white chart paper.
- Mark the rectangles 1, 2, 3 n, (n + 1) along the vertical line and 1,2, 3,…. n along the horLontal line.
- Colour the rectangular strips of length 1 cm, 2 cm, 3 cm n cm each of width 1 cm.
- Complete the rectangle with sides n and n+1. Name this rectangle as PQRS. Mark dot in each square as shown.
- Count the coloured squares and total number of squares in rectangle PQRS.
Observation
We observe, number of shaded squares =(1/2) x total no. of squares
No. of shaded squares = 1+ 2 + 3 + … + n
Total squares = Area of rectangle = n (n + 1)
Therefore 1 + 2 + 3 + … + n = (1/2)n(n + 1)
Mathematically
Area of rectangle PQRS = 10 x 11
Area of shaded region = (1/2) x 10 x 11 = 55 ……………….(i)
Also, area of shaded region = (1 x 1) + (2 x 1) + (3 x 1) +… + (10 x 1)
= 1+2 + 3 + … +10 = 55 …………………….(ii)
From (i) and (ii),
1+2 + 3 + … + 10=(1/2)x 10 x 11 = 55
Verified that 1 + 2 + 3 + … + 10 = (1/2)x 10 (10 + 1) by graphical method.
Result
It is verified graphically that 1 + 2 + 3 + … + n = (1/2)n(n+ 1) or sum of first n natural numbers =(1/2) n(n + 1).
Learning Outcome
Students will develop a geometrical intuition of the formula for the sum of natural numbers starting from one.
Activity Time
- Find the sum of first 100 natural numbers.
- Find the sum of first 1000 natural numbers.
- Evaluate 10 + 11 + 12 + … + 25.
Related Exams
About this Document
4.68/5
Rating
Apr 19, 2025
Last updated
Document Description: Lab Manual: Arithmetic Progression II for Class 10 2025 is part of Class 10 preparation. The notes and questions for Lab Manual: Arithmetic Progression II have been prepared according to the Class 10 exam syllabus. Information about Lab Manual: Arithmetic Progression II covers topics like and Lab Manual: Arithmetic Progression II Example, for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Lab Manual: Arithmetic Progression II.
Introduction of Lab Manual: Arithmetic Progression II in English is available as part of
our Class 10 preparation & Lab Manual: Arithmetic Progression II in Hindi for Class 10
courses. Download more important topics, notes, lectures and mock test series for Class 10
Exam by signing up for free. Class 10: Lab Manual: Arithmetic Progression II - Class 10
Description
Full syllabus notes, lecture & questions for Lab Manual: Arithmetic Progression II - Class 10 - Class 10 | Plus excerises question with solution to help you revise complete syllabus | Best notes, free PDF download
Information about Lab Manual: Arithmetic Progression II
In this doc you can find the meaning of Lab Manual: Arithmetic Progression II defined & explained in the simplest way possible.
Besides explaining types of Lab Manual: Arithmetic Progression II theory,
EduRev gives you an ample number of questions to practice Lab Manual: Arithmetic Progression II tests, examples and also practice Class 10 tests.
Download as PDF
Top Courses for Class 10
Related Searches
past year papers
,Free
,Summary
,Lab Manual: Arithmetic Progression II - Class 10
,Sample Paper
,Objective type Questions
,shortcuts and tricks
,Important questions
,Lab Manual: Arithmetic Progression II - Class 10
,mock tests for examination
,video lectures
,MCQs
,ppt
,study material
,Previous Year Questions with Solutions
,practice quizzes
,Lab Manual: Arithmetic Progression II - Class 10
,Viva Questions
,Extra Questions
,Exam
,Semester Notes
;
Additional Information about Lab Manual: Arithmetic Progression II for Class 10 Preparation
Lab Manual: Arithmetic Progression II Free PDF Download
The Lab Manual: Arithmetic Progression II is an invaluable resource that delves deep into the core of the Class 10 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Lab Manual: Arithmetic Progression II now and kickstart your journey towards success in the Class 10 exam.
Importance of Lab Manual: Arithmetic Progression II
The importance of Lab Manual: Arithmetic Progression II cannot be overstated, especially for Class 10 aspirants.
This document holds the key to success in the Class 10 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Lab Manual: Arithmetic Progression II Notes
Lab Manual: Arithmetic Progression II Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Lab Manual: Arithmetic Progression II.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Lab Manual: Arithmetic Progression II Notes on EduRev are your ultimate resource for success.
Lab Manual: Arithmetic Progression II Class 10 Questions
The "Lab Manual: Arithmetic Progression II Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Lab Manual: Arithmetic Progression II on the App
Students of Class 10 can study Lab Manual: Arithmetic Progression II alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Lab Manual: Arithmetic Progression II,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Lab Manual: Arithmetic Progression II is prepared as per the latest Class 10 syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup