Question

What is the sum of all positive integers that are multiples of 7 from 200 to 400?

Answer 1

203 + 210 + 217 + ... + 392 + 399 =

= 7(29 + 30 + 31 + ... + 56 + 57)

= 7(1 + 28 + 2 + 28 + 3 + 28 + ... + 28 + 28 + 29 + 28)

= 7(1 + 2 + 3 + ... + 28 + 29 + 28 * 29)

= 7(1 + 2 + 3 + ... + 28 + 29 + 812)

= 7 * 812 + 7 * (1 + 2 + ... + 28 + 29)

= 5684 + 7 * (29 * 30)/2

= 5684 + 3045

= 8729