Home
Class 12
MATHS
The ratio of the sums of m and n terms o...

The ratio of the sums of m and n terms of an A.P is `m^(2):n^(2)`. Show that the ratio of m^(th)` and `n^(th)` term is (2m-1) : (2n -1) .

A

`(2m+1):(2n-1),`

B

`m:n`

C

`(2m-1):(2n-1)`

D

None of these

Text Solution

Verified by Experts

(c) Here, `" "(S_(m))/S_(n)=(m^2)/(n^2) " "[therefore A=1,B=0]` S
` therefore " " (t_(m))/(t_(n))=((2m-1))/((2n-1))`
`implies t_(m):t_(n)= (2m-1):(2n-1)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The ratio of 7^(th) to 3^(rd) term of an A.P. is 12:5 . Find the ratio of 13^(th) to 4^(th) term.

If the sum of first n terms of an A.P. is cn^(2) , then the sum of squares of these n terms is :

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)^("th") " to " (2n)^("th") term is 1/r^n .

If the sum of n terms of A.P. is (1)/(2) (3n^(2) + 7n) , find its n^(th) term and write its 25th term.

Find the second term if sum of the 'n' tem of an AP is 2n^2 +1 .

Show that the sum of (m + n)^(th) and (m – n)^(th) terms of an A.P. is equal to twice the m^(th) term.

If the sum of n terms of an A . P is 3n^(2)+5n and its m^(th) term is 164 , find the value of m.

If the sum of n terms of an A.P. is given by S_(n)=n^(2)+n , then the common difference of the A.P. is

Write the first five terms if n^(th) term is a_(n)=n(n+2)

Write the first five terms if n^(th) terms is a_(n)=(2n-3)/(6)