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

If Sn=n2p and Sm=m2p, mn, in A.P., then Sp is?

A
p2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
p3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
p4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B p3
Sm=n2pSm=m2p
n2{2a+(n1)d}=n2p
2a+(n1)d=2np
2a+ndd=2np(1)
Sm=m2p
m2{2a+(m1)d}=m2p
2a+mdd=2mp(2)
subtract equation (2) from equation (1)
(2a+ndd)(2a+mdd)=2np2mp
d(nm)=2p(nm)
d=2p(3)
Put value of d from equation
(3) to equation (2)
2a+(m-1)(2p)=2 m p
a+mpp=mpa=p(4)
Sp=p2{2a+(p1)d}=p2{2p+(p1)2p}Sp=p3
Answer: option
(B)

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