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

In an A. P., Sm:Sn=m2:n2 . The ratio of p2th term to q2th term is:


A

2p2+12q2+1

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

2p2-12q2-1

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

2p-12q-1

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

p2-2q2-2

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

The correct option is B

2p2-12q2-1


Explanation for the correct option:

Step 1: Simplify Sm:Sn=m2:n2

Sm=m22a+m-1d [Sum of numbers in A.P]

and Sn=n22a+n-1d

Now,

m22a+m-1dn22a+n-1d=m2n2⇒m2a+m-1dn2a+n-1d=m2n2⇒2a+m-1d2a+n-1d=mn

By taking 2 common, from numerator and denominator, we get

a+m-12da+n-12d=mn...(1)

Step 2: Find the ratio of p2th term to q2th term.

Let m-12=p2-1andn-12=q2-1 then m=2p2-1andn=2q2-1

By substituting the value of mandn in 1, we get

a+p2-1da+q2-1d=2p2-12q2-1

The nth term of A.P is =a+n-1d. So, a+p2-1d will be the p2th term and a+q2-1d will be the q2th term.

p2thtermq2thterm=2p2-12q2-1⇒p2thtermq2thterm=2p2-12q2-1

Hence, option B is correct.


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