How to Solve Rational Numbers Sequence Problems

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Solving a rational numbers sequence always requires you to keep a few basic things in mind. Solve rational numbers sequences with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: College Math
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to solve rational number sequence problems. Now, oftentimes, when you have rational numbers in a sequence, that simply pretty much tells you that the rational numbers, which are fractions, can be a combination of mostly fractions, or you might throw some integers in there. Simply because, every integer, for example, if you have three, three can be thought of as three over one. But if you have rational numbers, you may have, negative five-sixths, two-thirds, just to name a few. Now, when it comes to solving rational number sequence problems, you still want to use the same kinds of formulas involving sequences, and let's just go over those real quickly. Now, if you have rational numbers which are part of an arithmetic sequence, terms separated by addition or subtraction, keep in mind this particular formula: "A N" is equal to A1 plus N minus one times D. Now, just to kind of refresh your memory, "A N" refers to the general term, or you can say "nth" term, if you like. A1 is the first term. N is whatever term that you're looking for. And D is the arithmetic difference. In other words, what number needs to be added/subtracted between each term to get to what you're looking for? What is the pattern, if you will, in the arithmetic sequence? Now, if it's a geometric sequence, you may have to use, A N is equal to A1, R to the N minus 1. Now, A N is the same as this A N, the general term, has the same meaning. A1 is also known as the first term. R is the geometric ratio. In other words, what number has to be multiplied/divided between the terms? And then you have N minus one. So, even if your terms are rational numbers here, when it comes to solving rational number sequence problems, you're most likely going to use one of these formulas, as long as you can kind of figure out what kind of sequence that we're talking about. And, even if you're not sure, plug into one of these, and then see what it is that you have. So, I'm Jimmy Chang, and that's how to solve rational number sequence problems.


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