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.
Let's try plugging in some negative numbers. Let's do x=-1. 5+-1=4. So we know that if we put in a negative number for x, then n will be positive. But what if we do a number greater than -5, because 5+-5=0. So let's try x=-6. So 5+(-6)=-1. Hmm. So here it is. We know that any number under -5 will be positive and any number above -5 will be negative.
