Question

What is the sum of the first 200 positive even integers?

Answer 1

2, 4, 6, 8, ................394, 396, 398, 400

Notice the pattern:
sum of first and last number is 402
sum of second and second to the last is 402
sum of third and third to last is 402

How many of these "pairs" are there? (the answer is 100)

Multiply 100 x 402 = 40200