Answer :

To prove: (a2 – b2), (b2 – c2), (c2 – d2) are in GP.


Given: a, b, c are in GP


Formula used: When a,b,c are in GP, b2 = ac


Proof: When a,b,c,d are in GP then



From the above, we can have the following conclusion


bc = ad … (i)


b2 = ac … (ii)


c2 = bd … (iii)


Considering (a2 – b2), (b2 – c2), (c2 – d2)


(a2 – b2) (c2 – d2) = a2c2 – a2d2 – b2c2 + b2d2


= (ac)2 – (ad)2 – (bc)2 + (bd)2


From eqn. (i) , (ii) and (iii)


= (b2)2 – (bc)2 – (bc)2 + (c2)2


= b4 – 2b2c2 + c4


(a2 – b2) (c2 – d2) = (b2 – c2)2


From the above equation we can say that (a2 – b2), (b2 – c2), (c2 – d2) are in GP


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
caricature
view all courses
RELATED QUESTIONS :

The product of thRD Sharma - Mathematics

Express <imRS Aggarwal - Mathematics

If a, b, c are inRS Aggarwal - Mathematics

Express <imRS Aggarwal - Mathematics

Prove that RS Aggarwal - Mathematics

If a, b, c are inRS Aggarwal - Mathematics

The sum of n termRS Aggarwal - Mathematics

If a, b, c, d areRS Aggarwal - Mathematics

Evaluate :
</p
RS Aggarwal - Mathematics

The first term ofRS Aggarwal - Mathematics