CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

If the (p+1)th, (q+1)th, (r+1)th terms of an AP are in GP when p, q, r are in HP, then the ratio of the first term to the common difference of the AP is

A

2q

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

-2q

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

-q/2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

q/2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

-q/2


Let the terms be a+pd, a+qd, a+rd where a is the first term of AP and d is common difference of AP. Now p,q,r are in HP, So, q=2pr(p+r) and also the terms are in GP. So (a+qd)2=(a+pd)×(a+rd). Solving this leaves us with (ad)=(q2rp)(p+r2q). Substituting p+r=2prq, we get ad=q2 .Hence, choice (c) is the right option

flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image