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
Show Answer
Answer:
Correct Answer: 2. (d)
Solution:
- 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.
