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Question

Suppose four distinct positive number $$a_1, a_2, a_3, a_4$$ are in G.P. Let $$b_1 = a_1, b_2 = b_1 + a_2, a_3 = b_2 + a_3 $$ 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.
Statement 2 - The numaber $$b_1, b_2, b_3, b_4$$ are in H.P.


A
Both Statement 1 and Statement 2 are correct and Reason is the correct explanation for Assertion
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B
Both Statement 1 and Statement 2 are correct but Statement 2 is not the correct explanation for Assertion
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C
Statement 1 is correct but Statement 2 is incorrect
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D
Both Statement 1 and Statement 2 are incorrect
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Solution

The correct option is D Statement 1 is correct but Statement 2 is incorrect
$$b_1 = a_1, b_2 = b_1 + a_2 = a_1 + a_2$$
$$b_3 = b_2 + a_3 = a_1 + a_2 + a_3, b_4 = a_1 + a_2 + a_3 + a_4$$
Clearly $$b_1, b_2, b_3, b_4$$ are neither in A.P. nor in G.P. Hence statement - 1 is true.
Also $$b_1, b_2, b_3, b_4$$ are not in H.P. Hence statement - 2 is false.

Mathematics

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