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General Sequences And Series - Example 3

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 for this one, it's going to be the third example out of our general sequences and Siri's Siri's. And we've got the question. Find the next five terms of the sequence in our sequence is a sub is equal to n factorial. So from here, if we have a some N is equal to n factorial. We know that in order to find our first five terms and one and two ends of three and four and ends of five, all we really have to do is plug in that 1234 and five for our end. So our aides of one is gonna be, Oh, a part of these. So our ace of one is just gonna be one factorial, which is just one. A sub two is going to be two factorial, which is two tons one So to ace of three is gonna be are three factorial which is going to be three times two times one, which is six and then for a set of four. We've got four factorial, which is four times three times two times one, which gives us 24 and for eight and five, we've got five factorial, which is five times, four times, three times, two times one, which is going to become 120. So here are our first five terms of that sequence. And again, it really was so much more about, like, determining kind of the pattern. Um, So from our pattern, we just kind of plug in the end value, whatever, whatever term that is into the factorial. And then we just saw that through.

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Anna Marie V.

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