If a,b,c,l,m are in
a.p then find value of a-4b+6c-4l+m
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Given,
a,b,c,l,m are in A.P.
Let, D is the common difference of the A.P.
So,
b=a+D
c=a+2D
l=a+3D
m=a+4D
Now,
Substitue the values of b,c,l and m in : a-4b+6c-4l+m, we get...
a-4b+6c-4l+m
=a-4(a+D)+6(a+2D)-4(a+3D)+(a+4D)
=a-4a-4D+6a+12D-4a-12D+a+4D
=a+a+6a-4a-4a+4D-4D+12D-12D
=8a-8a
=0
a,b,c,l,m are in A.P.
Let, D is the common difference of the A.P.
So,
b=a+D
c=a+2D
l=a+3D
m=a+4D
Now,
Substitue the values of b,c,l and m in : a-4b+6c-4l+m, we get...
a-4b+6c-4l+m
=a-4(a+D)+6(a+2D)-4(a+3D)+(a+4D)
=a-4a-4D+6a+12D-4a-12D+a+4D
=a+a+6a-4a-4a+4D-4D+12D-12D
=8a-8a
=0
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