Formulae for Geometric pogression
Mean ,one of the kind of averages,is generally defined for a set of data . The mean of data set is sum of the numbers divided by number of data elements.here is a tutoring on online geometric mean .
There are three types of calculation of means of data depending on the sequence of data.
i) Arithmetic Mean
iii) Harmonic mean
Geometric mean of a progression :-
The geometric mean is calculated for a geometric distribution .The Geometric distribution or progression is the sequence of numbers such that ratio of successive numbers is constant.The general geometric distribution is given as a, ad ,ad2 , . . . . . , ad(n-1). here initial number is "a" and common ratio is "d".
Here initial number is 1 and common ratio is 3.
The mean "b"of a geometric distribution a,b,c is given by b= [sqrt(a*c)]
Formulae for Geometric progressions or distribution (G.P):-
i) nth term of an G.P is a*r^(n-1) ii) sum to infinite terms of a G.P is a/(1-r) where r is <1 iii) If a,b,c are in geometric progression then b= [sqrt(a*c)] iv) Sum to numbers in G.P is a(1-r^n ) / (1-r)
Example problems on geometric mean :-
Ex 1)Find the geometric mean (G.M)of numbers 2,32
Solution)Geometric mean of two numbers is given by square root (32*2) =square root (64) =8
Hence G.M of two numbers is 2 ,32 is 8
Ex2)Find the geometric mean of geometric sequence 1,3,6,9
Solution)geometric mean of sequence 1,3,6,9 is
EX3)Find the geometric mean of distribution 2,4,8
Solution )Geometric mean is given by sqrt( 2*4*8)
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