Say we were tasked to find the sum of the series from 51 through 375 of a series whose values are all separated by a common difference of six. That's a difference of 324 so it would take 324 hops if the hops were each one in size, but the hops are six times bigger than that so it takes six times fewer hops. 324/6 = (300+24)/6 = 50 + 4 = 54. So note that there are 55 numbers in the series! Only one of the initial and last numbers corresponds to any of those hops (take your pick, it all depends on your perspective which one). In any case, there is one more stop than hop, considering that you are already at a stop before the first hop and you'll arrive at a stop after the last hop. Option A: We could subtract the first number from every number in the series, and end up with 55 of those subtracted terms. So we could compute our sum as 55*51 + 6,12,18...318, 324 The first part is as easy as (here's an easy way to multiply... read more