Given a,b,c,d are in G.P then $a^{2} - b^{2}, b^{2} - c^{2}, c^{2} - d^{2}$ are in ........

G.P

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A.G.P

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A.P

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H.P

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Solution

The correct option is A G.P
As $a, b, c, d$ are in G.P , then
$(a^{2} - b^{2}) (c^{2} - d^{2}) = a^{2} c^{2} + b^{2} d^{2} - (b^{2} c^{2} + a^{2} d^{2})$

$= b^{4} + c^{4} - 2 b^{2} c^{2} = (b^{2} - c^{2})^{2}$
Hence
$(a^{2} - b^{2}), (b^{2} - c^{2}), (c^{2} - d^{2})$ are in G.P

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