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If there are (2n+1) terms in A.P., then ...

If there are `(2n+1)` terms in A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is `(n+1): ndot`

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The correct Answer is:
`(n+1);n`
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Find the sum of n terms of an A.P. whose nth term is (2n+1).

Find the AP in which the ratio of the sum to n terms to the sum of succeding n terms is independent of n .

Knowledge Check

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

  • 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)`

  • If the sum of m terms of an A.P. is same as the sum of its n terms, then the sum of its (m+n) terms is

    A
    mn
    B
    `-mn`
    C
    1/mn
    D
    0

    • Similar Questions

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    Find the sum of 'n' terms of an A.P. whose nth term is 2n+1.

    Questions on Sum of n terms in A.P.

    The ratio of the sums of m terms and n terms of an A.P. is m^(2) : n^(2). Prove that the ratio of their mth and nth term will be (2m - 1) : (2n-1).

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

    If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m+n) terms is:

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