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

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