Question

Write the first five terms of the sequence defined by the explicit formula a subscript n baseline equals 21 minus 2 n squared.
(1 point)
Responses

21 comma 19 comma 13 comma 3 comma negative 11
Image with alt text: 21 comma 19 comma 13 comma 3 comma negative 11

20 comma 17 comma 12 comma 5 comma negative 4
Image with alt text: 20 comma 17 comma 12 comma 5 comma negative 4

23, 29, 39, 53, 71
23, 29, 39, 53, 71

19 comma 13 comma 3 comma negative 11 comma negative 29

Answer 1

To find the first five terms of the sequence defined by the formula \( a_n = 21 - 2n^2 \), we will calculate the terms for \( n = 1, 2, 3, 4, 5 \).

1. For \( n = 1 \):
\[
a_1 = 21 - 2(1^2) = 21 - 2(1) = 21 - 2 = 19
\]

2. For \( n = 2 \):
\[
a_2 = 21 - 2(2^2) = 21 - 2(4) = 21 - 8 = 13
\]

3. For \( n = 3 \):
\[
a_3 = 21 - 2(3^2) = 21 - 2(9) = 21 - 18 = 3
\]

4. For \( n = 4 \):
\[
a_4 = 21 - 2(4^2) = 21 - 2(16) = 21 - 32 = -11
\]

5. For \( n = 5 \):
\[
a_5 = 21 - 2(5^2) = 21 - 2(25) = 21 - 50 = -29
\]

Thus, the first five terms of the sequence are \( 19, 13, 3, -11, -29 \).

So the correct answer is:
**19, 13, 3, -11, -29.**