In AP, the nth term is calculated as:
An = A1 + (n-1)D, where D is the common difference

Using the same,
Let a be the first term in the AP, i.e A1. Then,
a = A1
b = A1 + 1*D = A1 + D
c = A1 + 2*D = A1 + 2D
d = A1 + 3*D = A1 + 3D
e = A1 + 4*D = A1 + 4D

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In AP, the nth term is calculated as:

An = A1 + (n-1)D, where D is the common difference

Using the same,

Let a be the first term in the AP, i.e A1. Then,

a = A1

b = A1 + 1*D = A1 + D

c = A1 + 2*D = A1 + 2D

d = A1 + 3*D = A1 + 3D

e = A1 + 4*D = A1 + 4D

To find, a – 4b + 6c – 4d + e

a – 4b + 6c -4d + e

= A1 – 4(A1+D) + 6(A1+2D) – 4(A1+3D) + (A1+4D)

= A1 – 4A1 – 4D + 6A1 + 12D – 4A1 + 12D + A1 + 4D

= 0