Question Video: Finding Terms of a Sequence Given the General Term Mathematics

Find the first 3 terms of the sequence whose general term π‘Ž_𝑛 = 𝑛/(𝑛 + 1).

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Video Transcript

Find the first three terms of the sequence whose general term π‘Ž sub 𝑛 is equal to 𝑛 over 𝑛 plus one.

We’ve been given a general term to find by π‘Ž with a little subscript 𝑛. This is sometimes called the 𝑛th term. The 𝑛th term of a sequence is an algebraic rule which allows us to find any term in that sequence based on the term number. And so, we can find the first three terms of the sequence by substituting into this formula three different values of 𝑛. Now, the first term of a sequence is when 𝑛 is equal to one, the second term is when 𝑛 is equal to two, the third is when 𝑛 is equal to three, and so on.

So, let’s do this in table form. We said that we can find the value of a term by substituting our value for 𝑛 into the formula 𝑛 over 𝑛 plus one. And so, the first term, which is when 𝑛 is equal to one is one over one plus one, which is equal to one-half. Then, we see that the second term is when 𝑛 is equal to two. So, it’s two over two plus one, which is two-thirds. Finally, the third term is three over three plus one, which is three-quarters.

The first three terms of the sequence with general term π‘Ž sub 𝑛 equals 𝑛 over 𝑛 plus one are one-half, two-thirds, and three-quarters.

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