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

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

01:58

Video Transcript

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

In order to calculate the first five terms of our sequence, we need to substitute 𝑛 equals one, two, three, four, and five into our expression for π‘Ž sub 𝑛. The first term is when 𝑛 equals one. We denote this as π‘Ž sub one, and it is equal to one squared minus 14. We know that one squared is equal to one, and subtracting 14 from this gives us negative 13. The first term of our sequence is therefore negative 13. To calculate the second term, we substitute 𝑛 equals two. This is equal to two squared minus 14. And as two squared is equal to four, this is equal to negative 10.

We can repeat this process to calculate the third, fourth, and fifth terms. When 𝑛 equals three, π‘Ž sub three is equal to negative five. When 𝑛 equals four, four squared minus 14 equals two. And finally, the fifth term π‘Ž sub five is equal to five squared minus 14, which equals 11. The first five terms of a sequence whose 𝑛th term is given by π‘Ž sub 𝑛 equals 𝑛 squared minus 14 are negative 13, negative 10, negative five, two, and 11.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.