Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

17. If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

Answers (1)

best_answer

Given: a, b, c, d are in G.P.

To prove:(a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

Then we can write,

     b^2=ac...............................1

    c^2=bd...............................2

   ad=bc...............................3

 

Let (a^n + b^n), (b^n + c^n), (c^n + d^n) be in GP

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

LHS:  (b^n + c^n)^2

(b^n + c^n)^2 =b^{2n}+c^{2n}+2b^nc^n

 (b^n + c^n)^2 =(b^2)^n+(c^2)^n+2b^nc^n                 

                      =(ac)^n+(bd)^n+2b^nc^n

                      =a^nc^n+b^nc^n+a^nd^n+b^nd^n

                       =c^n(a^n+b^n)+d^n(a^n+b^n)

                       =(a^n+b^n)(c^n+d^n)=RHS

Hence  proved 

Thus,(a^n + b^n), (b^n + c^n), (c^n + d^n) are in GP

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE board exams 2025 from February 15; Class 10, 12 subject-wise marks distribution
anam-khan

CBSE Date Sheet 2025: Class 10, 12 board exam dates soon on cbse.gov.in; previous trends, sample papers
anam-khan

CBSE Board Exams 2025: 75% attendance must for students to be eligible, reiterates board

Latest Question