Sequences & Series
AP identity; value of parameter
Grade Class 12
Question:
If $a$, $b$, $c$ are in AP and $(a+2b-c)(2b+c-a)(c+a-b)=\lambda abc$, then the value of $\lambda$ is
Step-by-Step Solution
Key Concept: Use $2b=a+c$ (AP condition). Substitute $a+2b-c=2a$, $2b+c-a=2c$, $c+a-b=b$.
$(2a)(2c)(b)=4abc$, so $\lambda=4$.
Correct Answer: 4