Error Correction College

By: Yugal Garg Robin Philip Prashant Kumar Shiwani Raghav Aamir Altaf Tanvi Agarwal

WHAT IS AN ARITHMETIC PROGRESSION? AN ARITHMETIC PROGRESSION (A.P.) IS A LIST OF NUMBERS IN WHICH EACH TERM IS OBTAINED BY ADDING A FIXED NUMBER d TO THE PRECEDING TERM, EXCEPT THE FIRST TERM. THE FIXED NUMBER d IS CALLED THE COMMON DIFFERENCE.

THE GENERAL FORM OF AN A.P. IS : a , a+d , a+2d , a+3d , . . . THE nth TERM an OF THE ARITHMETIC PROGRESSION WITH FIRST TERM a AND COMMON DIFFERENCE d IS GIVEN BY: an = a + (n - 1) d an IS ALSO CALLED THE GENERAL TERM OF THE ARITHMETIC PROGRESSION. IF THERE ARE m TERMS IN THE ARITHMETIC PROGRESSION , THEN am REPRESENTS THE LAST TERM WHICH CAN BE DENOTED BY l.

S 1 a 2 a+d 3 a+d+d 4 a+d+d+d 5 a+d+d+d+d 6 a+d+d+d+d+d 7 a+d+d+d+d+d+d 8 a+d+d+d+d+d+d+d 9 a+d+d+d+d+d+d+d+d 10 a+d+d+d+d+d+d+d+d+d

S d+d+d+d+d+d+d+d+d+a . d+ d + d + d + d + d + d + d + a d+d+d+d+d+d+d+a d+d+d+d+d+d+a d+d+d+d+d+a d+d+d+d+a d+d+d+a d+d+a d+a a

S + S = 2S 1 a d+d+d+d+d+d+d+d+d+a 2 a+d d+ d + d + d + d + d + d + d + a 3 a+d+d d+d+d+d+d+d+d+a 4 a+d+d+d d+d+d+d+d+d+a 5 a+d+d+d+d d+d+d+d+d+a 6 a+d+d+d+d+d d+d+d+d+a 7 a+d+d+d+d+d+d d+d+d+a 8 a+d+d+d+d+d+d+d d+d+a 9 a+d+d+d+d+d+d+d+d d+a 10 a+d+d+d+d+d+d+d+d+d a

S + S = 2S a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a

S + S = 2S d+d+d+d+d+d+d+d+d a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+ d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ d+d+d+d+d+d+d+d+d +a a+ +a 2S= 10a+ (10x9) d +10a ……………………………… 2S = 10a+90d+10a 2S = 20a+90d S = 10a+45d S = 5 x (2a+9d) S = 10 x [2a+(10-1)d] 2

S a a+ d a+ d + d a+ d + d+d a+ d + d+d+d a+ d + d+d+d+d .. .. .. a + d + d + d + d + d+ d +d+……d[(n-1)times]

s (n-1) times d+…d+d+d+d+d+a .. .. .. d+d+d+d+a d+d+d+a d+d+a d+a a

S + S = 2S [(n-1) times] d … d+d+d+d+d+d+a a .. a+ d .. a+ d + d .. a+ d + d+d a+ d + d+d+d d+d+d+d+a a+ d + d+d+d+d d+d+d+a .. d+d+a .. d+a .. a a + d + d + d + d + d+ d +d+…d[(n- 1)times]

S + S = 2S d + d+ d+ d ……...+ (n-1)d a+ +a …(1) d + d+ d+ d ………+ (n-1)d a+ +a …(2) d + d+ d+ d ………+ (n-1)d a+ +a a+ d + d+ d+ d ………+ (n-1)d .. +a .. .. .. .. .. d + d + d + d ………+ (n-1)d a+ +a ..(nth eqn) 2S= na + (n)(n-1) d + na 2S = na +(n)(n-1)d + na 2S = 2na + (n)(n-1)d S = na + (n)(n-1)d 2 S = n[2a + (n-1)d] 2

Method to calculate the sum of an arithmetic progression when the first and the last terms are known: We know that the sum of an arithmetic progression is given by: S = n [ 2a + (n-1)d ] 2 S = n [ a + a + (n-1)d ] 2 We know that the last term l can be written as [ a + (n-1)d ] Therefore S=n[a+l] 2

Acknowledgement 1. Dr. Sanjeev Agrawal 2. Dr. Amber Habib 3. Niteesh Sahni 4. Shivani Wadehra 5. Sanat Upadhyay 6. Manisha Bhardwaj 7. Zia Ur Rahman 8. Charu Sharma 9. Ajaz Ahmed 10.Reyaz Ahmed

BIBLIOGRAPHY The information and the images for the PowerPoint presentation on ARITHMETIC PROGRESSIONS has been taken from: 1) MATHS NCERT FOR CLASS X 2) www.google/images.com 3) digital-photography-school.com 4) photoshop-manic.blogspot.com

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Error Correction College

by Anjani on Apr 13, 2010

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Error Correction College — Presentation Transcript