Given 3, - 6,9, - 12... - 20042007 write the 100th number in this column? Find the sum of the number in this column? | Math enthusiast | Mathematical art

Given 3, - 6,9, - 12... - 20042007 write the 100th number in this column? Find the sum of the number in this column?

an=-(-1)^n*3*n
a100=-3*100=-300
S=3-6+9-12.+2007
S=3*(1-2+3-4+..+667-668+669)
=3*[(1-2)+(3-4)+..+(667-668)+669]
=3*[(-1)*334+669]
=3*335
=1005

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