Question : If a, b, c form a A.P. with common difference d, then the value of a-2b-c is equal to
a) 2a+4d
b) 0
c) -2a-4d
d) -2a-3d
Doubt by Vikrant
Solution :
a, b, c are in AP (Given)
d=common difference
We know,
an=a+(n-1)d
a =a
a2=a+d
b=a+d — (1)
a3=a+2d
c=a+2d — (2)
a-2b-c
=a-2(a+d)-(a+2d)
[Substituting the values of a and from equation (1) and (2)]
=a-2a-2d-a-2d
=a-3a-4d
=-2a-4d
[Substituting the values of a and from equation (1) and (2)]
=a-2a-2d-a-2d
=a-3a-4d
=-2a-4d
Hence, c)-2a-4d, would be the correct option.