Question Video: Finding the Value of a Term in a Sequence given the General Term of That Sequence Mathematics

Find the eighth term of the sequence whose 𝑛th term is given by π‘Ž_(𝑛) = (6/3𝑛) βˆ’ 2, where 𝑛 ∈ ℀⁺.

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Video Transcript

Find the eighth term of the sequence whose 𝑛th term is given by π‘Ž sub 𝑛 equals six over three 𝑛 minus two, where 𝑛 is in the set of positive integers.

The 𝑛th term or the general term here will allow us to find the value of any term in the sequence. The value of 𝑛 represents the index of the term in the sequence. We are given the information that 𝑛 is in the set of positive integers. So that means that the first term in the sequence will have an index of one. If we did want to find the first three terms in the sequence, for example, we would substitute in the values of 𝑛 equals one, two, and three in turn into the 𝑛th term.

But here, we’re just asked for one specific term, the eighth term. And so we must substitute the value of 𝑛 equals eight into the 𝑛th term. This gives us π‘Ž sub eight, the eighth term, is equal to six over three times eight minus two. Simplifying, we have six over 24 minus two. And of course, six over 24 simplifies to one-quarter. In order to evaluate one-quarter minus two, we need to convert two into a fraction over four. And so we have one-quarter subtract eight-quarters.

And so we can give the answer that the eighth term of the sequence with 𝑛th term π‘Ž sub 𝑛 equals six over three 𝑛 minus two is negative seven over four.

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