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.
This is a question that can be solved with Pythagorean Theorem since it is a right triangle. The longest side, 29, is the hypotenuse and the sides 21 and x are the legs. So, the Pythagorean Theorem states,
Where,
c is the Hypotenuse, a and b are the legs. Putting the respective values gives us,
You can set of an equation of 45 - x = 111 x representing the amount of miles Nicole drove. You would subtract 45 from both 45 and 111 and get that x = 66.
