If Sₙ₊₂ − Sₙ₋₂ = 286, what is the value of n?

Correct answer: 71

Answer: D, 71. The sum Sₙ₊₂ contains all numbers from 1 through n + 2, while Sₙ₋₂ contains all numbers from 1 through n − 2. Subtracting cancels the common terms 1 through n − 2. The four terms left are n − 1, n, n + 1, and n + 2. Their sum is (n − 1) + n + (n + 1) + (n + 2) = 4n + 2. Equating this with 286 gives 4n + 2 = 286, so 4n = 284 and n = 71. Thus option D is correct. A direct check is helpful: if n = 71, the remaining terms are 70, 71, 72, and 73, whose sum is 70 + 71 + 72 + 73 = 286. Option A gives 68, option B gives 69, and option C gives 70; each produces a four-term sum smaller than 286. The key counting point is that the index gap is four, so four terms remain.