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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. - Mathematics and Statistics

Sum

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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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Sequences and Series
Miscellaneous Exercise 2 | Q II. (31) | Page 42
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