Introduction
A series is called Geometric Progression (GP) when there ratio are same across service between consecutive number.
Ex. 1, 2, 4, 8 ……………….
Ration between 1 and 2 = 2/1=2
Ratio Between 2 and 4 = 4/2 = 2 and so on….
Here, Ratio is called as Common Ratio and we represent it as r.
Formulas at a Glance
- Formula to find out nth term of the GP Series –
Where a = First Term of the Series, r = Common Ratio and n= Number of term
- Formula to Calculate Sum Of GP series –
Where Sn = Sum pf n Term, a = First Term of the Series, r = Common Ratio and n= Number of term.
Also, We apply this formula when r > 1
- Forma to Calculate Sum Of GM when r is infinite Value
Where a = First Term of the Series, r = Common Ratio and n= Number of term.
Important Facts
The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant. This relationship allows for the representation of a geometric series using only two terms, r and a. The term r is the common ratio, and a is the first term of the series. As an example the geometric series given in the introduction,
may simply be written as
,
and
-
A repeating decimal can be viewed as a geometric series whose common ratio is a power of 1/10.
- There are many uses of geometric sequences in everyday life, but one of the most common is in calculating interest earned.
Tutorial Video(s)
Part1
Exercise 1
