The first and last two terms of an A.P. are a,b,c respectively in order. Then the sum of all the term is
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a,b,c...
common difference=d
a+d=b
a+2d=c
sum=a+b+c
=a+a+d+a+2d=3a+3d
a+c=a+a+2d=2a+2d
b+c-2a=a+d+a+2d-2a=2a+3d-2a=3d
2(b-a)=2(a+d-a)=2d
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