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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 for Statement -1.

B

Statement -1 is true, Statement -2 is True, Statement -2 is not a correct explanation for Statement for Statement -1.

C

Statement -1 is true, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

Verified by Experts

The correct Answer is:
C
Let r be the common ratio of the G.P.
We have,
`b_(1)=a_(1),b_(2)=a_(1)+a_(2)=a_(1)(1+r),b_(3)=b_(2)+a_(3)=a(1+r+r^(2))`,
`b_(4)=b_(3)+a_(4)=a_(1)(1+r+r^(2)+r^(3))`
Clearly, `b_(1),b_(2),b_(3),b_(4)` are neither in A.P. nor in G.P.
So, statement -1 is correct.
Also, `b_(1),b_(2),b_(3),b_(4)` are not in H.P. So, statement -2 is false.
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