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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): n`

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We have to prove the ratio of sum of odd terms to sum of even terms of an arithmetic series to be `(n+1)/n`
Since there are` 2n+1` terms there will be `n+1`terms.
Let us consider the odd terms and even terms to be two different series.
These series will have common difference` 2d, `where d is the common difference of original series.
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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

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