Answer :

Let us suppose a and b are two numbers.

Let us say G is the Geometric mean of a and b.

a, G and b must be in Geometric Progression or GP.

This means, common ratio = G/a = b/G

Or, G2 = ab

Or, Gn = n(ab) ............ (1)

Now, let us say G1 , G2 , G3 ,.......Gn are n geomteric means between a and b.

Which means that

a , G1 , G2 , G3 ...... Gn , b form a G.P.

Note that the above GP has n+2 terms and the first term is a and last term is b, which

is also the (n+2)th term

Hence, b = arn+2-1`

where a is the first term.


b = arn+1


Now the product of GP becomes

Product = G1G2G3......Gn

= (ar)(ar2)(ar3)..(arn)

= an.r(1+2+3…+n)


Putting the value of r from equation 2 , we get


= .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

If AM and GM of tRD Sharma - Mathematics

If AM and GM of rRD Sharma - Mathematics

Write the quadratRS Aggarwal - Mathematics

<span lang="EN-USRD Sharma - Mathematics

Find the two numbRD Sharma - Mathematics

Insert 5 geometriRD Sharma - Mathematics

If a, b, c are inRD Sharma - Mathematics

Prove that the prRD Sharma - Mathematics

Construct a quadrRD Sharma - Mathematics

If a, b, c are inRD Sharma - Mathematics