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Show that the sum of (m + n)^(th) and (...

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.

Text Solution

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The correct Answer is:
`2 a_(n)`
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The (m+n)^(th) and (m-n)^(th) terms of a G.P. are p and q respectively. Show that the m^(th) and n^(th) terms are sqrtpq and p((q)/(p))^((m)/(2n)) respectively.

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Knowledge Check

  • If 10^(th) and 4^(th) terms of a G.P are 9 and 4 respectively, then its 7^(th) term is…….

    A
    6
    B
    36
    C
    `(4)/(9)`
    D
    `(9)/(4)`

  • If 3^(rd) and 10^(th) terms of an A.P. be 9 and 21 respectively. Then the sum of its first 12 terms is…….

    A
    180
    B
    360
    C
    150
    D
    210

  • The p^(th), q^(th) and r^(th) terms of an A.P. are in geometric progression then common ratio for G.P is…….

    A
    `(p-q)/(q-r)`
    B
    `(q-r)/(p-q)`
    C
    pqr
    D
    None of these

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    Explore conceptually related problems

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    If (x + 1), 3x and (4x + 2) are first three terms of an A.P. then its 5^(th) term is

    If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(1/m-1/p)=(m+p)(1/m-1/n)dot

    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 .

    Find the 31th term of an AP whose 11th term is 38 and the 16th term is 73.

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