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! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B

-2q

No worries! Weâ€˜ve got your back. Try BYJUâ€˜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! Weâ€˜ve got your back. Try BYJUâ€˜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)=(q2−rp)(p+r−2q). Substituting p+r=2prq, we get ad=−q2 .Hence, choice (c) is the right option

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Fear of the Dark
QUANTITATIVE APTITUDE
Watch in App
Explore more
Join BYJU'S Learning Program