# If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Given: 4th, 10th and 16th terms of a G.P. are x, y and z, respectively

Let a be the first term and r be the common ratio of the G.P.

Here,

We know that nth term of the G.P is given by arn-1

a4 = ar3 = x —1

a10 = ar9 = y —2

a16 = ar15 = z —3

Dividing eq-(2) by eq-(1), we obtain

Dividing eq(3) by eq-(2), we obtain

That is

Thus, x, y, z are in G. P

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive quiz on inequalities involving AM and GM45 mins
Check Your progress Part 2| Interactive Quiz: Sequence & Series47 mins
Sequence & Series (Lecture 1)56 mins
Sequence & Series (Lecture 5)42 mins
Sequence & Series (Lecture 7)37 mins
Sequence & Series (Lecture 6)42 mins
AM, GM & HM | How are they related?59 mins
Use of sigma in finding sum42 mins
Trigonometric Series45 mins
Quick Recap lecture of Sequence & Series56 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
view all courses