Arithmetic progression

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Question

$if a,b,c are in A.P and (a + 2 b - c) (4 b + 2 c - 2 a) (c + a - b) = λ abc,then the value of λ is$

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Solution

$C o n s i d e r t h e e x p r e s s i o n (a + 2 b - c) (4 b + 2 c - 2 a) (c + a - b) \sin c e a, b, c a r e i n A P 2 b = a + c (a + a + c - c) (2 a + 2 c + 2 c - 2 a) (2 b - b) = 2 a \cdot 4 c \cdot b = 8 a b c$
$hence λ=8$

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