Original subtitles

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Today we're going to be talking about how to list the first several terms of a sequence.

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And in this particular problem we've been asked to list the first five terms given that a sub 1 is equal

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to one and a formula here for a sub and plus one at the end plus one term which we've been given as

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5 a sub n minus 3.

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So it a problem like this when we're listing the first several terms the first thing we want to do is

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start constructing a table of values.

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We know here that our first term a sub one is equal to one so let's go ahead and write that down a sub

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1 is equal to 1.

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Now we need to find the next term in the sequence Well that's going to be a sub 2 and we don't know

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the value of it yet but we know that it's going to be one greater than a sub one.

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So we've got here a sub 2.

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Okay so how do we find a sub 2.

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We're going to be using the formula for a sub and plus one.

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Well if we're using this formula here for Aisyah then plus one we know since this is plus one.

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And this is n that the value of a sub and plus one is dependent on the previous value.

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Subban right.

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Because A-7 is exactly one less than a sub and plus one.

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So a 7 is going to be US plugging in the previous value that we found.

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So to find a sub 2 we're going to get five right which comes directly from our ace and plus one formula

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times a sob in the previous term.

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Thats a sub once we multiply that by one there because the value of a sub one is one and then we go

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ahead and subtract three.

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So what we get there then is a sub 2 is equal to 2 5 minus 3 which is 2.

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So now we have a value for a sub to a sub 3 the next value is going to involve the exact same formula

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but now are going to be using a sub to the previous term before a sub 3s are going to get five times

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our previous value here for a sub to 2.

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And then we're going to subtract 3 there that's going to give us 10 minus 3.

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And we know that a sub 3 is equal to 7 and we just keep going like this until we have the first five

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terms of our sequence so a sub 4 will be 5 times the previous value 7 minus 3.

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That will give us 35 minus 3 or a sub 4 is equal to thirty two and finally a sub 5 the fifth value or

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the fifth term in our sequence will give us 5 times 30 to minus three which is going to give us 160

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minus 3 or subtype is equal to one fifty seven and we could just continue on like that for however many

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terms we were asked to list.

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So thats how you use the first time in a sequence and a formula for the end plus 1 term to list the

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first several terms in the sequence.