2+（-4）+6+（-8）+10+（-12）+...+994+（-996）+998+（-1000）=?

2+（-4）+6+（-8）+10+（-12）+...+994+（-996）+998+（-1000）=?

2+（-4）+6+（-8）+10+（-12）+...+994+（-996）+998+（-1000）
=（2-4）+（6-8）+（10-12）………… （998-1000）
= -2X250
= -500

2-4+6-8+10-12…… +994-996+998-1000=?

2-4+6-8+10-12…… +994-996+998-1000
=(2-4)+(6-8)+(10-12).(994-996)+(998-1000)
=(-2)×（1000÷2÷2）
=-500
Note: from 1 to 1000, there are 1000 △ 2 = 500 even numbers. When two even numbers are combined together, there are 500 △ 2 = 250 even pairs. The sum of each even pair is (- 2), so the answer is - 500

2, - 4,6, - 8,10, - 12,14, - 16. What is the 1000th number

a(1)=2
a(2)=-4
a(3)=6
a(4)=-8
So:
a(n)=(2n)*(-1)^(n+1)
So:
a(1000)=2000*(-1)^1001=-2000