Find the first five terms of a
sequence whose 𝑛th term is given by 𝑎 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 𝑎 sub 𝑛. The first term is when 𝑛 equals
one. We denote this as 𝑎 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, 𝑎 sub three
is equal to negative five. When 𝑛 equals four, four squared
minus 14 equals two. And finally, the fifth term 𝑎 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 𝑎 sub 𝑛 equals 𝑛 squared minus 14 are negative 13,
negative 10, negative five, two, and 11.