Suppose four distinct positive numbers a_1, a_2, a_3, a_4 are in G.P. Let b_1 = a_1, b_2 = b_1 + a_2, b_3 = b_2 + a_3 and b_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. and STATEMENT-2 : The numbers b_1, b_2, b_3, b_4 are in H.P.

JEE Advanced 2008 Mathematics question

Suppose four distinct positive numbers , , , are in G.P. Let , , and . STATEMENT-1 : The numbers , , , are neither in A.P. nor in G.P. and STATEMENT-2 : The numbers , , , 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 FalseCorrect
(D)STATEMENT-1 is False, STATEMENT-2 is True

Answer: (C)

Solution

Let (r > 0, r ≠ 1). Then , , , . A.P. would need , i.e. r = r², impossible. G.P. would need , i.e. , i.e. r

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Question ID VK-037614