Question Video: Finding Certain Terms in a Sequence given Its General Term Mathematics

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž_(𝑛) = 5/(𝑛 βˆ’ 12).


Video Transcript

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž sub 𝑛 equals five over 𝑛 minus 12.

The 𝑛th term here is equivalent to the general term of the sequence. The value of 𝑛 represents the index of the terms. Let’s assume here that the index values of 𝑛 take values which are greater than or equal to one. That means that the first term has an index of one, the second term has an index of two, and so on. And so to find the first five terms in the sequence, we substitute the values of 𝑛 equals one, two, three, four, and five in turn into the formula for the 𝑛th term.

The first term can be written as π‘Ž sub one. And so substituting 𝑛 is equal to one into the formula, we have π‘Ž sub one is equal to five over one minus 12. We can then simplify this as five over negative 11, and that’s equivalent to negative five over 11. So that’s the first term in the sequence.

The second term in the sequence will be π‘Ž sub two, and that will be equal to five over two minus 12. Simplifying this, we have five over negative 10. We can write this equivalently as negative one-half. The third term π‘Ž sub three is equal to five over three minus 12. This is equal to five over negative nine, which is the same as negative five-ninths.

We could then work out π‘Ž sub four and π‘Ž sub five as five over four minus 12 and five over five minus 12, respectively, giving us the values of negative five-eighths and negative five-sevenths. We can then give the answer that the first five terms in this sequence are negative five elevenths, negative one-half, negative five-ninths, negative five-eighths, and negative five-sevenths.

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