Question

if the numbers a,b,c,d and e from an AP then find the value of a -4b+6c-4d+ e solve this​

Answer 1

Let D be the common difference of the given A.P. Then,

b=a+D,c=a+2D,d=a+3D and e=a+4D

∴a−4b+6c−4d+e=a−4(a+D)+6(a+2D)+(a+3D)+(a+4D)

⟹a−4b+6c−4d+e=a−4a−4D+6a+12D−4a−12D+a+4D

⟹a−4b+e=a−4a+6a=4a+a−4D+12D−4a−12D+a+4D

⟹a−4b+6a−4d+e=0