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  4. 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 find the value of λ.

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Q. If $a, b, c$ are in A.P. and $(a+2 b-c)(4 b+2 c-2 a)(c+a-b)=\lambda$ abc, then find the value of $\lambda$.

Sequences and Series

Solution:

Let $ a = A - d $
$b = A $
$c = A + d $
$\therefore(2 A -2 d )(4 A +4 d )( A )=\lambda( A - d ) A ( A + d ) $
$\text { Hence, } \lambda=8$