Question

Write the first five terms in the sequence defined by the explicit formula a subscript n baseline equals n squared minus 2.
(1 point)
Responses

negative 1 comma 2 comma 7 comma 14 comma 23
Image with alt text: negative 1 comma 2 comma 7 comma 14 comma 23

1, 4, 9, 16, 25
1, 4, 9, 16, 25

1, 0, 1, 4, 9
1, 0, 1, 4, 9

negative 2 comma negative 1 comma 2 comma 7 comma 14

Answer 1

To find the first five terms in the sequence defined by the formula \( a_n = n^2 - 2 \), we can calculate \( a_n \) for \( n = 1, 2, 3, 4, \) and \( 5 \):

1. For \( n = 1 \):
\[
a_1 = 1^2 - 2 = 1 - 2 = -1
\]

2. For \( n = 2 \):
\[
a_2 = 2^2 - 2 = 4 - 2 = 2
\]

3. For \( n = 3 \):
\[
a_3 = 3^2 - 2 = 9 - 2 = 7
\]

4. For \( n = 4 \):
\[
a_4 = 4^2 - 2 = 16 - 2 = 14
\]

5. For \( n = 5 \):
\[
a_5 = 5^2 - 2 = 25 - 2 = 23
\]

Putting it all together, the first five terms of the sequence are:

\(-1, 2, 7, 14, 23\)

Thus, the correct answer is:

**negative 1, 2, 7, 14, 23**