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General Sequences And Series - Example 4

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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Video Transcript

Okay, so this one is going to be our fourth example out of our general sequences and Siri's Siri's, and it says, find the next five terms of Siri's. We've got 10.51 3rd, 0.25 And so here's our first term second term, third term and fourth term. So we have to find our fifth term, our sixth term or seventh term, our eighth term and our ninth term. So in doing so, let's just go ahead and think about the patterns that air there. And just so keep in mind that we have basically just to look for the patterns and it's a lot of times just like a trial and error type of situation. So in doing so, I see that my, um, currently I have some integer integer of fraction and some decimals, so I'm gonna try to get everything consistent and make everything a fraction, because that might help me see what the trend is. Um or actually, let's start with decimal. If we did that, I get 10.50 point 33 and 0.25 and I'm not necessarily seeing any sort of a trend here. Um, because going from here, we subtracted 0.5 or two. Here we subtracted 0.17 going to hear we subtracted 0.8. So in that sense, I don't really see a lot going on. So instead, let's go ahead and backtrack and rewrite it as factions because once we do that, I'm going to get 1/1 1/2, 1/3 and whatever. Four. So now I'm really trying to I'm really starting to see that the trend is like one over end. So for 1/5 term is gonna be 1/5 for 1/6 term. It's gonna be 1/6. Our seventh term is gonna be 1/7 or eight. Term is gonna be won over eight or ninth term is gonna be won over nine. So these are our next five terms of Siri's. And just like this, we basically just tried a couple of different things and kind of try to see if they would work based off of the patterns that we saw. And when we first started started with the decimal, we didn't really see much. And so we try something else. So that should be Your mindset is like first at first. If it doesn't work out, just try something else until it works, so