Suppose four distinct positive numbers $a_1, a_2, a_3$ and $a_4$ are in GP. Let $b_1=a_1$, $b_2=b_1+a_2,…

Suppose four distinct positive numbers $a_1, a_2, a_3$ and $a_4$ are in GP. 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 $b_1, b_2, b_3$ and $b_4$ are neither in AP nor in GP.
Statement 2 The numbers $b_1, b_2, b_3$ and $b_4$ are in HP.
  1. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  2. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  3. Statement 1 is true, Statement 2 is false.
  4. Statement 1 is false, Statement 2 is true

Solution

Let $a_1=1, a_2=2, a_3=4, a_4=8$ $ \therefore b_1=1, b_2=3, b_3=7, b_4=15 $ Clearly, $b_1, b_2, b_3$ and $b_4$ are not in HP. Statement 2 is false

Asked in: JEE Advanced 2008 (Paper 2)

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