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If p^(th), q^(th), r^(th) and s^(th) te...

If `p^(th), q^(th), r^(th) and s^(th)` terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

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The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q-r) a+(r-p) b+(p-q)c = 0

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Knowledge Check

  • 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

  • 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)`

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    If the 2nd, 5th and 9th term of A.P. are in G.P, then the common ratio of this GP is

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    If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

    If the 4^(th) and 7^(th) term of a G.P. are 27 and 729 respectively, then find the G.P.

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