# If a, b, c, d are in a G.P., then prove that a + b, b + c, c + d, are also in G.P.

Proof: a, b, c, d are in G.P

a = a, b = ar ,c = ar2,d = ar3.

To prove: a + b, b + c, c + d, are also in G.P, if-

(a + b) (c + d) = (b + c)2

Now, we need to prove : (a + b) (c + d) = (b + c)2

L.H.S. = (a + ar)(ar2 + ar3)

= a(1 + r) ar2 (1 + r)

= a2r2 (1 + r)2

R.H.S. = (ar + ar2)2

= (ar(1 + r))2

= a2r2 (1 + r)2

L.H.S = R.H.S

Hence, proved that-

(a + b) (c + d) = (b + c)2

a + b, b + c, c + d, are also 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:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
Fundamental Theorem of Arithmetic- 143 mins
Euclids Division Lemma49 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Quiz | Imp Qs on Real Numbers37 mins
Relation Between LCM , HCF and Numbers46 mins
Application of Euclids Division Lemma50 mins
Quiz | Fun with Fundamental Theorem of Arithmetic51 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