Home
Class 12
MATHS
If the arithmetic progression whose comm...

If the arithmetic progression whose common difference is nonzero the sum of first `3n` terms is equal to the sum of next `n` terms. Then, find the ratio of the sum of the `2n` terms to the sum of next `2n` terms.

A

`(1)/(5)`

B

`(2)/(3)`

C

`(3)/(4)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given, common difference`ne0`
`S_(3n)=S_(4n)-S_(3n)`
`implies2*S_(3n)=S_(4n)" " [" let " S_(n)=Pn^(2)+Qn]`
`implies2*[P(3n)^(2)+Q(3n)]=P(4n)^(2)+Q(4n)`
`implies 2Pn^(2)+2Qn=0`
or `Q=-nP" " "….(i)"`
`:.(S_(2n))/(S_(4n)-S_(2n))= (P(2n)^(2)+Q(2n))/([P(4n)^(2)+Q(4n)]-[P(2n)^(2)+Q(2n)])`
`=(2n(2nP+Q))/(12Pn^(2)+2nQ)=(2nP+Q)/(6nP+Q)`
`=(2nP-nP)/(6nP-nP)=(1)/(5)" " [" from Eq. (i) "]`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

In an AP, the sum of first ten terms is - 150 and the sum of its next ten terms is - 550. Find the AP.

If the sum of the first ten terms of an A.P is four times the sum of its first five terms, the ratio of the first term to the common difference is:

The sum of the first 7 terms of an AP is 63 and the sum of its next 7 terms is 161. Find the 28th term of this AP.

Find an A.P whose sum of n terms is equal to three times the square of n.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

If the sum of first n terms of an AP is cn^(2) , then the sum of squares of these n terms is

The sum of first n terms of an AP is 5n^2 + 3n If its mth term is 168, find the value of m. Also find the 20th term of the AP.

in a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals-