Video: Finding the Terms of a Sequence given Its General Term

Find the first five terms of the sequence whose general term is given by 𝑎_𝑛 = 4𝑛 + 1, where 𝑛 ≥ 1.

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Video Transcript

Find the first five terms of the sequence whose general term is given by 𝑎 sub 𝑛 is equal to four 𝑛 plus one, where 𝑛 is greater than or equal to one.

So here is our general term of our sequence. And we’re asked to find the first five terms. So in order to find terms, we need to plug in values into this general term to find our sequence. So where do we begin when plugging in numbers? Well, they tell us that 𝑛 is greater than or equal to one. So since it’s equal at one and then greater than one, we can start by plugging in one. So we will begin by replacing 𝑛 with one. Four times one plus one. Well, four times one is four and four plus one is five. So the first term in our sequence is five.

Now, to find our next term, let’s plug in two. Four times two plus one. Four times two is eight and eight plus one is nine. So our next term in this sequence is nine. Now, we plug in three. Four times three is 12 and 12 plus one is 13. So 13 is our third term. Now, we have four times four plus one, which is 16 plus one. So our fourth term is 17. And then, lastly, we will find our fifth and final term by plugging in five. Four times five is 20 and 20 plus one is 21. Therefore, the first five terms of this sequence would be five, nine, 13, 17, and 21.

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