wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the pth,qth,rth terms of a H.P. be a,b,c respectively, prove that
(qr)bc+(rp)ca+(pq)ab=0.

Open in App
Solution

Given that a,b,c are the pth,qth.rth terms of a H.P

1a,1b,1c are the pth,qth.rth terms of an A.P

Let the A.P have x as the first term and d as the common difference
1a=x+(p1)d ----1

1b=x+(q1)d ----2

1c=x+(r1)d ----3

1-2 we get 1a1b=(pq)d

d=baab(pq)

Similarly
2-3 we get d=cbbc(qr)

3-1 we get d=acac(rp)

d=baab(pq)=cbbc(qr)=acac(rp)

We know that if x=ab=cd=ef then x=a+c+eb+d+f

d=ba+cb+acab(pq)+bc(qr)+ac(rp)

d=0ab(pq)+bc(qr)+ac(rp)

(ab(pq)+bc(qr)+ac(rp))d=0

ab(pq)+bc(qr)+ac(rp)=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon