ap_patternsnew1

8/3/2019 AP_patternsnew1

http://slidepdf.com/reader/full/appatternsnew1 1/18



OUTLINE OUTLINE

Introduction

Some patterns of AP

Real life problems in AP

Conclusion

References



INTRODUCTION:INTRODUCTION:

ARITHMETIC PROGRESSIONSARITHMETIC PROGRESSIONS

Arithmetic Progressions is a

sequence of numbers such that the

difference between the consecutiveterms is constant.

For instance 3,5,7,9,11,13,15««.

The above sequence is an

Arithmetic Progressions with

constant difference of 2.



S SOME OME PPATTERNSATTERNS OF OF

ARITHEMETIC PROGRESSIONARITHEMETIC PROGRESSION



SECTORS OF CIRCLE IN AP

Angles of the

sectors shown in

the Fig. 1 are in

AP. Angles 30Ý, 60Ý,

90Ý, 120Ý are in

AP havinga= 30Ý, d= 30Ý

n=4Fig. 1



Cubes in AP

oThe cubes shown in

the adjacent Fig.2 are

in AP.

oTheir dimensionsare decreasing in AP

as 5,4,3,2, cm sides

respectively as going

from top to bottom.

oThis has: a=5, d=

²1 and n=4

Fig.2



CIRCLES IN AP

Radii of Circles

shown in the Fig.

3 are in AP.

Radii aredecreasing as

6,5,4,3,2,1 which

are in AP.With a= 6, d= ²1

and n=6Fig .3



CIRCLES IN AP

Radii of Circlesshown in the

Fig. 4 are in AP.

Radii areincreasing as

2,4,6,8,10 cm.

which are in AP.

With a= 2, d= 2

n= 5

Fig. 4



TRIANGLE IN AP

Fig. 5

Length of side of

equilateral Triangles

shown in the Fig. 5

are in AP.Length of sides are

increasing as

6,7,8,9cm. whichare in AP.

With a= 6, d= 1 , n=

4



PENTAGONS IN AP

Length of sides of

regular hexagon

shown in the Fig. 6

are in AP.Length of sides are

increasing as

2,4,6,8,10cm.

which are in AP.With a= 2,d= 2, n= 5

Fig. 6



Apex angles of Triangles shown in

the Fig. 7 are in AP.

Angles are in series

30Û, 50Û,70Û, 90Û, 110Ûwhich are in AP.

Series with a= 30Û

d= 20Û and n= 5

APEX ANGLES OF TRIANGLES IN AP

Fig.7



EQUILATRAL TRIANGLES IN AP

Equilateral Triangles

shown in the Fig. 6 are

in AP.

Length of sides of triangles are increasing

as 3,4,5,6,7 cm. which

are in AP.

With a= 3,d= 1, n= 5

Fig. 8



Rhombus shown inthe Fig. 9 are in AP.

Sides of rhombus are

4,6,8 cm. (starting

from inside) whichare in AP.

AP with a= 4 d= 2 and

n=3

RHOMBUS ARE IN AP

Fig.9



ARITHMETIC

PROGRESSIONS AND ITS

EXAMPLES IN DAILY LIFE



Y ou must have observed that in nature many

things follows certain pattern, such as the petals

of the sunflower, the holes of honey bee comb, thegrains in maize cob the spirals of the pineapple

and pine cone etc.some of them follow AP.

Even the great structures such as Taj and

architectural buildings follow some or the otherpatterns to become unique.resting pillers and

arches follow AP.

Daily life salary annual increments of parents

and savings also the budget of mothers followsome patterns as the prizes of items hike in the

market. looking into such examples AP can be

found easily.



CONCLUSIONSCONCLUSIONS

It is seen from the AP series that a

fixed increase or decrease in a quantity

or data gives linear change in the given

quantity or data. Hence the patterns

shown in the presentation is quite

rhythmic. Real life problems is also

explored.



REFERENCESREFERENCES

owww.authorstream.com/Presentation/tanyase

hgal-564700- arithmetic-progression

ohttp://mathematicsprojects.blogspot.com/2008/12/mathematical-designs-using-ap.html



THANK YOU

ap_patternsnew1

Documents