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Question
Answer the following:
If p, q, r, s are in G.P., show that (pn + qn), (qn + rn) , (rn + sn) are also in G.P.
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Solution
p, q, r, s are in G.P.
`"q"/"p" = "r"/"q" = "s"/"r"`
`"q"^"n"/"p"^"n" = "r"^"n"/"q"^"n" = "s"^"n"/"r"^"n"`
∴ `("q"^"n" + "r"^"n")/("p"^"n" + "q"^"n") = ("r"^"n" + "s"^"n")/("q"^"n" + "r"^"n")`
∴ pn + qn, qn + rn, rn + sn are in G.P.
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