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

If l=1+a+a2+,,, to m=1+b+b2+... to , n=1+c+c2+... to where |a|<1,|b|<1,|c|<1 and a, b, c are in AP then l,m,n are in

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

The correct option is B HP
Here , l,m,n are the sum of infinite GP,
Therefore,
l=11a,m=11b,n=11c

On solving this , we get
a=l1l, b=m1m , c=n1n ........(1)

As a,b,c are in AP,
So, 2b=a+c .......(2)

Substitute values of a,b,c from (1) in (2). We get,
2(m1)m=n1n+l1l

=> 22m=11n+11l
=> 2m=1n+1l

Therefore, l,m,n are in HP.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon