0

Guest

Courses New

If pth , qth, rth term of an AP are in GP , then common ratio of this GP is (p-q)/(q-r) (q-r)/(p-q) pqr none of this

If pth , qth, rth term of an AP are in GP , then common ratio of this GP is 
  1. (p-q)/(q-r)
  2. (q-r)/(p-q)
  3. pqr
  4. none of this

Grade:11

2 Answers

moumi roy
91 Points
7 years ago
as this is in AP 2q=p+r----eq(1)
as in GP q=p.c & r=p*c2 where  c=common difference,
putting in eq(1) 2*p.c=p+p*c2 hence c^2+1-2c=0 or ( c-1)2=0 so c=1
frm(1) p-q=q-r or (p-q)/(q-r)=1=c or(q-r)/(p-q)=1=c so both can be the answer
 
Tushar Avhad
19 Points
6 years ago
Given that. pth ,qth,rth. Terms of an ap are in gp..therefore a+(q-1)d. a+(r-1)d-------------------- = -----------------(since they are a+(p-1)d. a+(q-1)d. Are in gp)Now,Let a+(q-1)d. a+(r-1)d-------------------- = -----------------= k a+(p-1)d. a+ (q-1)dBy theorem on equal ratiosWe geta+ qd-d -(a+rd-d)----------------------------=ka+pd-d-(a+qd-d)On simplifying we get qd-rd------------------=k pd-qd d(q-r)----------=kd(p-q) Therefore (q-r)-------------=k (P-q)Hope this will help u

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More