Question

If $a,b,c,l,m$ are in A.P., then the value of $a-4b+6c-4l+m$ is

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is D $0$

Since $a,b,c,l,m$ are in A.P, therefore,

$a+m=2c........\left(1\right)$

$b+l=2c.........\left(2\right)$

Now, consider

$a-4b+6c-4l+m$

$=a+6c+m-4(b+l)$

$=a+m+6c-4\left(2c\right)$ (using (2))

$=2c+6c-4\left(2c\right)$ (using (1))

$=8c-8c$

$=0$

Hence $a-4b+6c-4l+m=0$