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General Sequences And Series - Overview

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

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Okay, So in this video, we're going to be talking about general sequences in Siris. So with any general sequences in Siris, um, the most important thing is patterns and kind of recognizing them. So a lot of the times with general sequences in Syria, something that is not arithmetic or geometric. Or maybe it is, um, what's gonna happen is you're going to be able to you're gonna have to be forced to recognize the pattern. So sometimes you might be given, like a Sikh like a four first terms. And you have to find the next couple of terms or something like that. And in those cases, you have to try to recognize the pattern, and it really is kind of like a trial and error type of process where you just kind of have to try something. And if it works, then great. And if it doesn't work, then you could just go to try something else. So, um, a lot of patterns that might happen is adding and subtracting by something, whether that be directly so, for instance, if I had like 2468 then it's very clear that we're adding to each time But it's not always that obvious. Maybe it might be like to for AIDS. Um, maybe we're doing 248 and then 16, something like that, where we're supposed Thio, um, to on. Then add four and then add eight. And then we have to add more and more each time. So something like that, Yeah. So Okay, so in that sense, um, you might be having integers. You might also not have integers. So, for instance, you might have like, pie, and then I'm one over. Pi are Maybe we have one of her pie one over pi squared one of her pie. Cute eso There's a lot of different things that could be asked in this case you would be able to see that. Okay, well, this was one of her pie to the first one over Pi squared one over Pi Cube. So the next one realistically would be one of her pipe the fourth. And if you were to define, that would be one of her pie to the end. So in that sense, there's just infinitely many combinations that you could be asked about, but you basically just have to figure out what it would be by recognizing the patterns and just trial and error

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