# The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.

Given: 5th, 8th and 11th terms of a G.P. are p, q and s, respectively

We know that in G.P an = arn-1

Here, n: number of terms

a: First term

r: common ratio

Here,

a5 = ar5-1 = ar4

p = ar4 ( 5th term of G.P. is given p) –1

Similarly,

a8 = ar8-1 = ar7

q = ar7 ( 7th term of G.P. is given q) –2

a11 = ar11-1 = ar10

s = ar10 ( 11th term of G.P. is given s) –3

We can observe that:

q × q = p × s (that is, ar7 × ar7 = ar4 × ar10)

q2 = ps

Hence proved

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
Trigonometric Series45 mins
Use of sigma in finding sum42 mins
Quick Recap lecture of Sequence & Series56 mins
General Term of Miscellaneous progression46 mins
Improve your understanding of AP & GP27 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