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In an A.P,the sum of m terms of an AP is...

In an A.P,the sum of m terms of an AP is n and sum of n terms of AP is m,then prove that sum of (m+n) terms of AP is-(m+n)

Text Solution

Verified by Experts

Let a be the first term and d be the common difference of the `A.P`
Then,
`S_m​=n`
`=>m/2​{2a+(m−1)d}=n`
`=>2am+m(m−1)d=2n->(i)`
and, `S_n​=m`
...
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If in an AP,the sum of m terms is equal to n and sum of n terms is equal to m.Then prove that sum of (m+n) terms is -(m+n)

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Knowledge Check

  • 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:

    A
    mn
    B
    m+n
    C
    2(m+n)
    D
    `-(m+n)`

  • 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

  • If the mth term of an AP is 1/n and nth term is 1/m, then find the sum to mn terms.

    A
    ( mn – 1)/4
    B
    (mn + 1)/4
    C
    (mn + 1)/2
    D
    (mn - 1)/2

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    If the sum of m terms of an AP is the same as the sum of its n terms , show that the sum of its (m+n) terms is zero .

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    The sum of m and n terms of an A.P. are n and m respectively. Prove that the sum of (m + n) terms will be - (m+n).

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