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General Form of an AP

If a, b, c be...

Question

If a, b, c be in arithmetic progression, then the value of $(a + 2 b - c) (2 b + c - a) (a + 2 b + c)$ is

16 a b c

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4 a b c

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8 a b c

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3 a b c

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Solution

The correct option is A $16 a b c$
Since, a, b, c are in AP
$∴ 2 b = a + c$
Now, $(a + 2 b - c) (2 b + c - a) (a + 2 b + c)$
$= (a + a + c - c) (a + c + c - a) (2 b + 2 b)$
$= 2 a .2 c .4 b$
$= 16 a b c$

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