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General Form of an AP

If a,b,c are ...

Question

If $a, b, c$ are in arithmetic progression, then $\frac{1}{b c}, \frac{1}{a c}, \frac{1}{a b}$ will be in

A

Arithmetic progression

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B

Geometric progression

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C

Harmonic progression

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D

None of these

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Solution

The correct option is A
Arithmetic progression

Explanation for the correct option:
Given, $a, b, c$ are in arithmetic progression,
If we divide the numbers in arithmetic progression with the same number, the resulting numbers will also be in arithmetic progression.
Divide by $a b c$ with all variable
$\frac{a}{a b c}, \frac{b}{a b c}, \frac{c}{a b c} \frac{1}{b c}, \frac{1}{a c}, \frac{1}{a b},$
Which are in arithmetic progression
Hence, correct option is (A).

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