The difference between consecutive terms (numbers that come after each other) in arithmetic sequences is the same. That means you add the same number every time to get the next number. To figure out which choices are arithmetic sequences, just see if the differences are the same.
Choice A) 1, -2, 3, -4, 5, ... -2 - 1 = -3 3 - (-2) = 5 The difference is not constant, so it is not an arithmetic sequence.
Choice B) 12,345, 12,346, 12,347, 12,348, 12,349, ... 12,346 - 12,345 = 1 12,347 - 12,346 = 1 The difference is constant, so it is an arithmetic sequence.
Choice C) <span>154, 171, 188, 205, 222, ... 171 - 154 = 17 188 - 171 = 17 The difference is constant, so it is an arithmetic sequence.
Choice D) </span><span>1, 8, 16, 24, 32, ... 8 - 1 = 7 16 - 8 = 8 </span>The difference is not constant, so it is not an arithmetic sequence. Choice E) <span>-3, -10, -17, -24, -31, ... -10 - (-3) = -7 -17 - (-10) = -7 </span>The difference is constant, so it is an arithmetic sequence.
The reason for the columns adding up to 1 is that each individual consumes a proportion or a fraction of the total quantity produced under each product category and every product is consumed. There is no leftover.
When the proportions of all the individuals are added up, the sum is always 1 under each product category because each individual can only consume a part of the whole.
