Q. 55.0( 2 Votes )

If and terms of a G.P. are x, y, z respectively, then write the value of .

Answer :


Let the first term be a and the common ratio be R.


According to the question,


ap = x.


aq = t


ar = z.


We know that an = aRn-1


ap = aRp-1= x


aq = aRq-1= y


ar = aRr-1= z


xq-r = (aRp-1)q-r


yr-p = (aRq-1)r-p


zp-q = (aRr-1)p-q


Multiplying the above three equations we get


xq-r.yr-p.zp-q = (aq-r.Rpq-pr-q+r). (ar-p.Rrq-pq-r+p). (ap-q.Rpr-qr-p+q)


=(aq-r+r-p+p-q.Rpq-pr-q+r+rq-pq-r+p+pr-qr-p+q)


= (a0.R0)


= 1.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Geometric ProgressionGeometric ProgressionGeometric Progression58 mins
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
caricature
view all courses