Q. 145.0( 1 Vote )

# If a, b, c, d are in a geometric sequence, then show that (a - b + c) (b + c + d) = ab + bc + cd.

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

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

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

= a2r (1 + r2 + r4 )

And, R.H.S = a2r + a2r3 + a2r5

= a2r (1 + r2 + r4 )

L.H.S = R.H.S

Hence, proved that-

(a - b + c) (b + c + d) = ab + bc + cd.

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
Quiz | Imp Qs on Real Numbers37 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Application of Euclids Division Lemma50 mins
Relation Between LCM , HCF and Numbers46 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