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GP

I.   a, ar, ar2, ar3, ….. is a G.P.
 

First Term = a.
 

Common Ratio = r
 

In this G.P., we have –
 

(i)  an = arn – 1
 

(ii)        Sn =

 

        =  when r > 1
 

(iii)   Sum of an infinite G.P. =

 


 

 


II.      
It is Convenient to take
 

(i) three numbers in G.P. as , a, ar
 

(ii)    Four numbers in G.P. as ,, ar, ar2
 

(iii)   Five numbers in G.P. as , , a, ar, ar2

 

 


 

III.            Geometric mean between a and b is given by –
 

G.M. = .

 

 


IV.              If a, a1, a2, …, an, b are in G.P., then a1, a2, a3, ……, an are called the n geometric means between a and b.

 





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