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General Sequences And Series - Example 2

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 this is gonna be the second example. Second example, out of our general sequences in Syria's Siri's. And the question says, find the next five terms of the sequence. This one is pretty straightforward because we have an equation defined for us. So if we want to find the first term, for example, we would just plug in on end of one. So end of one means first term. So if we do a someone that is going to give us negative 6/1 plus three, which gives us negative 6/4, that gives us negative 3/2. So this is my first terms, and someone is equal to negative three over to. So then let's find our ends up to so ASAP to is going to become negative. 6/2 plus three, which is negative. 6/5. The negative six or five is our second term. So then saying with the third term you just plug in three for and again. So the negative 6/3 plus three gives us negative 6/6, which is negative one. So are third term is negative one, and we still have to find our 4th and 5th terms and which again, it's pretty easy because we just have to plug it into the equation that were already given. So if we do that, we would have a So four is equal to negative 6/4 plus three. So that gives us negative 6/7. So that's going to be our ends up four. And finally, for our ends of five, we have a sub five is equal to negative 6/5 plus three, which is negative. 6/8, which simplifies down to negative 3/4. These right here are gonna be our first five terms of that sequence.

Johns Hopkins University
Precalculus

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Top Precalculus Educators
Lily A.

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Megan C.

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Heather Z.

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