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

If a, b, c, l, m are in A.P, then

b-a = c-b = l-c = m-l.

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

a-b-b-b-b + c + c + c + c + c + c-l-l-l-l + m

Grouping the terms

We have

a + 4(c-b)-2(l-c)-2l + m

a + 2(c-b)-2(l-c) + 2(c-b)-2l + m

Since c-b = l-c,

a + 2(c-b)-2l + m

a + 2c-2b-2l + m

-(b-a) + (c-b)-(l-c) + (m-l)

= 0

So, the correct option is D.