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

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž_(𝑛) = 𝑛² βˆ’ 14, where 𝑛 β‰₯ 1.

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Video Transcript

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž sub 𝑛 is equal to 𝑛 squared minus 14, where 𝑛 is greater than or equal to one.

In order to calculate the first five terms of any sequence, where 𝑛 is greater than or equal to one, we need to substitute one, two, three, four, and five into the 𝑛th term formula. This will give us values for π‘Ž sub one through π‘Ž sub five, which are the first five terms of the sequence.

When 𝑛 is equal to one, we have one squared minus 14. One squared is equal to one. And subtracting 14 from this gives us negative 13. When 𝑛 is equal to two, we have two squared minus 14. As two squared is equal to four, this gives us an answer of negative 10. Three squared is equal to nine. And subtracting 14 from this gives us negative five. When 𝑛 is equal to four, we get an answer of two. Finally, the fifth term of the sequence is equal to five squared minus 14, which is 11.

The first five terms of the sequence whose 𝑛th term is π‘Ž sub 𝑛 equals 𝑛 squared minus 14 are negative 13, negative 10, negative five, two, and 11.

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