This document discusses geometric progressions and provides examples of their use. Geometric progressions are sequences where each term is multiplied by a constant ratio. This ratio is called the common ratio. Geometric progressions can model growth patterns like populations over time. Examples shown include smallpox outbreaks, US population growth, and marriage and divorce rates. Geometric progressions are useful for predicting future trends, understanding starting points, and setting goals for companies or other applications involving compound growth or decay over time.

1. Welcome In
Pawneshwar Datt Rai
Helping Site
Now We Are Going to Present The
Use Geometric Progression...
By – Pawneshwar Datt Rai

2.  Geometric
Progression is a
multiple Progression.
 In Geometric
Progression every
term multiple by
some constant
number.
 In Geometric
Progression
multiplied content no
called common ratio.
In above Picture we can see the term
Of Geometric Progression..
Here..
a = First Term
r = Common Ratio
For Getting Common Ratio we use
This Rule
r = An/An-1
By – Pawneshwar Datt Rai

3. Sum Of Geometric Progression
For Getting Sum Of Geometric Progression we use Two rule
In That Particular Rule
S is sum of the Geometric progression
U1 is the First term of Geometric Progression
r is common ratio of that Progression
n is the no of term in that Progression
First rule use when r>1, And second's is when r<1
By – Pawneshwar Datt Rai

4. served.
Country
Marriage
rate1 Divorce rate2
Australia 5.4 2.7
Austria 4.6 2.4
Belarus 7.1 3.2
Belgium 4.0 3.0
Bulgaria 3.9 1.5
Chile3 3.6 N/A
Cuba 4.9 3.0
Czech Republic 4.8 3.2
Denmark 6.5 2.9
Estonia 4.2 2.9
Finland 5.0 2.6
France 4.6 2.1
Germany 4.6 2.6
Greece 5.5 N/A
Hungary 4.5 2.5
Ireland4 5.1 0.7
Israel N/A N/A
Italy 4.5 0.7
Japan 5.8 2.2
Korea, South 6.4 3.5
Latvia 4.3 2.1
Lithuania 4.9 3.1
Luxembourg 4.4 2.3
Mauritius 8.8 1.0
Mexico 5.6 0.6
The Netherlands 5.0 1.9
Turkey N/A N/A
Ukraine 7.8 3.7
United Kingdom 5.1 2.8
United States 7.7 N/A
Venezuela 2.9 N/A
Data are for the latest year available.
N/A = data not available.
1. Marriage rates are the number of legal (recognized) marriages performed and registered
per 1,000 population.
2. Divorce rates are the number of final divorce decrees granted under civil law per 1,000
population.
3. Divorce was legalized in November 2004.
4. Ban on divorce was lifted by a referendum in 1995.
Source: United Nations (UN).
Few application of Geometric Progression..
Here First Picture Showing the Growth rate of smallpox (WHO)
And second picture showing the growth rate of US population during 19th-20th century (US census Bureau)
And third picture showing the growth rate between Marriage And Divorce Rate (UN)
By – Pawneshwar Datt Rai

5. 2007
Birth per 1000
population
Deaths per
1000
Population
Net Migrants
on per 1000
Population
Rate of natural
increase % Growth Rate
Africa 35.1 13.4 0.1 2.17 2.18
North America 16.6 7.2 1.0 0.94 1.04
South America 17.9 6.1 -0.3 1.18 1.15
Asia 19.1 7.0 -0.4 1.21 1.17
Europe 10.2 11.7 1.1 -0.15 -0.04
Oceania 16.2 7.3 2.5 0.89 1.14
World 20.1 8.4 -0.1 1.17 1.17
Source: United States Census Bureau.
World Population Vital Rates
By – Pawneshwar Datt Rai

6.  Use Of Geometric Progression...
After watching these Picture We Found Something
1 = With this progression we find the growth
of any particular Firm or company.
2 = With this progression we can guess the
future of any firm or company.
3 = With this progression we find the starting
stage of a company.
4 = With this progression we set the goal of a
company
By – Pawneshwar Datt Rai

7. Urban Population Growth
Urbanization (percent of total population in urban areas at mid-year) Urban Population (millions)
Average Annual Rate of Change in Urban
Population (per cent)
Country 1975 2000 Projected 2025 1975 2000 Projected 2025 1975-2000 Projected 2000-2025
Asia
Total 24 37.1 51.1 574.8 1,363.00 2,414.40 3.5 2.3
Bangladesh 9.9 23.2 36.3 7.2 29.9 70.2 5.7 3.4
China 17.4 35.8 56.9 161.4 455.8 819.7 4.2 2.3
India 21.3 27.7 37.3 132.4 282.5 520.2 3 2.4
Indonesia 19.3 42 65.9 26 87.9 173.8 4.9 2.7
Iran 45.7 64.2 76 15.3 42.6 67.7 4.1 1.9
Japan 56.8 65.2 71.7 63.4 82.8 89.5 1.1 0.3
Korea, South 48 79.6 85.2 16.9 37.2 42.2 3.2 0.5
Pakistan 26.3 33.1 46.2 18 47.3 106 3.9 3.2
Philippines 35.6 58.5 74.6 14.9 44.4 81.4 4.4 2.4
Thailand 23.8 31.1 42.2 9.8 19.1 30.7 2.7 1.9
World
Total 37.2 46.7 57.5 1,515.90 2,844.80 4,542.40 2.5 1.9
More developed
regions
66.9 73.2 79.3 700.5 874 990.3 0.9 0.5
Less developed regions 26.9 40.3 53.4 815.3 1,970.80 3,552.00 3.5 2.4
Source: UN Population Division.
Geometric series and geometric progressions have many applications
in the physical, biological, and social sciences, as well as in
investments and banking. Many problems in compound interest and
annuities are easily solved using these concepts.
By – Pawneshwar Datt Rai

8.  If Any one have any suggestion please fill
Free to suggest me.
 Hope This PPT will useful for all of you.
 If you like this PPT then apply it in your
life for any kind of use such as our given
example.
By – Pawneshwar Datt Rai

9. Thanks Very Much.
A happy and Prosperous day to all friends.
By – Pawneshwar Datt Rai