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In an A.P. with first term 'a' and the c...

In an A.P. with first term 'a' and the common difference `d(a, d!= 0)`, the ratio `'rho'` of the sum of the first `n` terms to sum of `n` terms succedding them does not depend on `n`. Then the ratio `(a)/(d)` and the ratio `'rho'`, respectively are

A

`(1)/(2), (1)/(4)`

B

`2, (1)/(3)`

C

`(1)/(2), (1)/(3)`

D

`(1)/(2), 2`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • In a arithmetic progression whose first term is alpha and common difference is beta , alpha,beta ne 0 the ratio r of the sum of the first n terms to the sum of n terms succeending them, does not depend on n. Then which of the following is /are correct ?

    A
    `alpha: beta = 2:1`
    B
    If `alpha " and " beta ` are roots of the equation `ax^2+bx+c =0` then `2 b^2 = 9ac`
    C
    The sum of infinite `G.P 1+r+r^2 + …. Is 3//2`
    D
    If `alpha =1` , then sum of 10 terms of A.P is 100

  • If the number of terms of an A.P. is (2n+1) , then what is the ratio of the sum of the odd terms to the sum of even terms ?

    A
    `(n)/(n+1)`
    B
    `(n^(2))/(n+1)`
    C
    `(n+1)/(n)`
    D
    `(n+1)/(2n)`

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