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Question

Assertion :Let three distinct positive real numbers a,b,c are in G.P., then a2,b2,c2 are in G.P. Reason: If we square each term of a G.P., then the resulting sequence is also in G.P.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
If we square each term of a G.P., then the resulting sequence is also in G.P.
Proof:
a,b,c are in G.P.
ba=cb .........(1)
For, a2,b2,c2
b2a2=ba×ba
=cb×cb (from eq. (1))
=c2b2
Thus a2,b2,c2 will also be in GP.

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