Home
Class 11
MATHS
If in an AP, S(n)= qn^(2) and S(m) =qm^...

If in an AP, `S_(n)= qn^(2)` and ` S_(m) =qm^(2)` , where `S_(r)` denotes the of r terms of the AP , then `S_(q) ` equals to

A

`(q^(3))/(2)`

B

mnq

C

`q^(3)`

D

`(m+n)q^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `S_(n)= qn^(2) and S_(m) =qm^(2)`
`therefore S_(1)=q.,s_(2)=4q.S_(2)=$q, S_(3)=9q and s_(4)=16q`
Now ` T_(1)=q`
`T_(2)=S_(2)-S_(1)=4q-q=3q`
`T_(3)=S_(3) -s_(2) =9q-4q=5q`
`T_(4) =S_(4)-S_(3)=16q-9q=7q`
So the series is q, 3q,5q,7q,.....
Here ,` a=q and d=3q-q=2q`
`S_(q)=(q)/(2)[2xxq(q-1)2q]`
`=(q)/(2) xx[2q+2q^(2)-2q]=(q)/(2)xx2q^(2)=q^(3)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    NCERT EXEMPLAR|Exercise Fillers|3 Videos

  • SEQUENCE AND SERIES

    NCERT EXEMPLAR|Exercise True / false|5 Videos

  • SEQUENCE AND SERIES

    NCERT EXEMPLAR|Exercise long answer type questions|4 Videos

  • RELATIONS AND FUNCTIONS

    NCERT EXEMPLAR|Exercise True /False|5 Videos

  • SETS

    NCERT EXEMPLAR|Exercise TRUE AND FALSE|6 Videos

Similar Questions

Explore conceptually related problems

If in an A.P.S_(n)=n^(2)q and S_(m)=m^(2)q, where S_(r) denotes the sum of r terms of the A.P.then S_(q) equals (q^(3))/(2) b.mnq c.q^(3) d.(m^(2)+n^(2))q

If in an A.P., S_n=n^2p and S_m=m^2p , where S_r denotes the sum of r terms of the A.P., then S_p is equal to 1/2p^3 (b) m n\ p (c) p^3 (d) (m+n)p^2

If in an A.P.S_(n)=n^(2)p and S_(m)=m^(2)p, then S_(p) is equal to

in an A.PS_(4)=16,S_(6)=-48 (where S_(n) denotes the sum of first n term of A.P then S_(10) is equal to

If S_(n), denotes the sum of n terms of an AP, then the value of (S_(2n)-S_(n)) is equal to

in an AP,S_(p)=q,S_(q)=p and S_(r) denotes the sum of the first r terms.Then S_(p+q)=

Second term of the AP if the S_(n) = n^(2) +n is ………

S_(r) denotes the sum of the first r terms of an AP.Then S_(3d):(S_(2n)-S_(n)) is -