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Question

Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1=a1, b2=b1+a2, b3=b2+a3 and b4=b3+a4.STATEMENT-1 : The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P.STATEMENT-2 : The numbers b1, b2, b3, b4 are in H.P.

A
STATEMENT1 is True, STATEMENT2 is True; STATEMENT2 is a correct explanation for STATEMENT1
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B
STATEMENT1 is True, STATEMENT2 is True; STATEMENT2 is NOT a correct explanation for STATEMENT1.
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C
STATEMENT1 is True, STATEMENT2 is False
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D
STATEMENT1 is False, STATEMENT2 is True
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Solution

The correct option is B STATEMENT1 is True, STATEMENT2 is Falsea1=k,a2=kr,a3=kr2,a4=kr3b1=k,b2=k+kr,b3=k+kr+kr2,b4=k+kr+kr2+kr3Thus, it is obvious that b1,b2,b3,b4 are neither in AP nor in GP.Again, 1b1+1b3=1k+1k+kr+kr2≠2k+kr=2b2Hence, b1,b2,b3 are not in HP.Hence, (C) is correct.

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