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Suppose four distinct positive numbers a...

Suppose four distinct positive numbers `a_(1),a_(2),a_(3),a_(4)` are in G.P. Let `b_(1)=a_(1)+,a_(b)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)andb_(4)=b_(3)+a_(4)`.
Statement -1 : The numbers `b_(1),b_(2),b_(3),b_(4)` are neither in A.P. nor in G.P.
Statement -2: The numbers `b_(1),b_(2),b_(3),b_(4)` are in H.P.

A

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1

B

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1

C

Statement 1 is true, Statement 2 is false

D

Statement 1 is false, Statement 2 is true

Text Solution

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The correct Answer is:
C
`b_(1)=a_(1),b_(2)=b_(1)+a_(2)=a_(1)+a_(2),b_(3)=b_(2)+a_(3)=+a_(1)+a_(2)+a_(3)`
and `b_(4)=b_(3)+a_(4)=a_(1)+a_(2)+a_(3)+a_(4)`
Hence, `b_(1),b_(2),b_(3),b_(4)` are neither in AP nor in GP and nor in HP.
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