Home
Class 11
MATHS
In an AP it is given that S(n)=qn^(2)an...

In an AP it is given that ` S_(n)=qn^(2)and S_(m) =qm^(2). " prove that " s_(q) = q^(3)`

Text Solution

Verified by Experts

`S_(n)=qn^(2)Rigtharrow S_(1)=q and S_(2) =4q`
`Rightarrow T_(1) = q and T_(1)+T_(2) =4q Rightarrow T_(1)=q and T_(2) =3q`
` S_(q) = q/2 xx [2q + (q-1) xx2q] = (q/2 xx 2q^(2))=q^(3)`
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION

    RS AGGARWAL|Exercise Exercise 11E|6 Videos

  • APPLICATIONS OF CONIC SECTIONS

    RS AGGARWAL|Exercise EXERCISE 25|5 Videos

  • BINOMIAL THEOREM

    RS AGGARWAL|Exercise EXERCISE 10B|16 Videos

Similar Questions

Explore conceptually related problems

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

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

If S_(m)=m^(2) p and S_(n)=n^(2)p , where m ne n in an AP then prove that S_(p) =P^(3)

If S_(n)=3n^(2)+2n, Then prove that series is in A.P

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 the sum of n terms of an AP is given by S_(n)=3n+2n^(2) then common difference of the AP is

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

a. If in an A.P. S_(1)=6 and S_(7)=105 prove that : S_(n),S_(n-3)::(n+3);(n-3) b. In an A.P., S_(3)=6 and S_(6)=3 prove that: 2(2n+1)S_(n+4)=(n+4)S_(2n+1) .

The sum of the first n terms of an AP is given by S_(n) = 3n^(2) — 4n . Determine the AP and the 12th term.