Sequences and Series 5 Question 2

2. If the positive numbers $a, b, c, d$ are in AP. Then, $a b c, a b d, a c d, b c d$ are

(2001, 1M)

(a) not in $AP / GP / HP$

(b) in AP

(c) in GP

(d) in HP

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Answer:

Correct Answer: 2. (d)

Solution:

  1. Since, $a, b, c, d$ are in AP.

$\Rightarrow \quad \frac{a}{a b c d}, \frac{b}{a b c d}, \frac{c}{a b c d}, \frac{d}{a b c d}$ are in AP.

$\Rightarrow \quad \frac{1}{b c d}, \frac{1}{c d a}, \frac{1}{a b d}, \frac{1}{a b c}$ are in AP.

$\Rightarrow \quad b c d, c d a, a b d, a b c$ are in HP.

$\Rightarrow \quad a b c, a b d, c d a, b c d$ are in HP.



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