Answer:
9900
Explanation:
Take each group of 4 consecutive integers and find their sum. Since there is a total of 200 numbers, there are 50 groups of 4 numbers.
1 + 2 + 3 - 4 = 2
5 + 6 + 7 - 8 = 10
9 + 10 + 11 - 12 = 18
13 + 14 + 15 - 16 = 26
...
197 + 198 + 199 - 200 = 394
We see a pattern.
2 + 10 + +18 + 26 + ... + 394
a_1 = 2; a_50 = 394; d = 8
Now we sum the terms of this series of 50 terms.
S_n = (n/2)(a_1 + a_n)
S_50 = (50/2)(2 + 394)
S_50 = 9900