Question

Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

an = –8n^2 − 3n + 2

Answer 1

To find the first five terms of the sequence defined by the formula \( a_n = -8n^2 - 3n + 2 \), we can substitute the values of \( n \) from 1 to 5 into the formula.

1. For \( n = 1 \):
\[
a_1 = -8(1^2) - 3(1) + 2 = -8(1) - 3 + 2 = -8 - 3 + 2 = -9
\]

2. For \( n = 2 \):
\[
a_2 = -8(2^2) - 3(2) + 2 = -8(4) - 3(2) + 2 = -32 - 6 + 2 = -36
\]

3. For \( n = 3 \):
\[
a_3 = -8(3^2) - 3(3) + 2 = -8(9) - 3(3) + 2 = -72 - 9 + 2 = -79
\]

4. For \( n = 4 \):
\[
a_4 = -8(4^2) - 3(4) + 2 = -8(16) - 3(4) + 2 = -128 - 12 + 2 = -138
\]

5. For \( n = 5 \):
\[
a_5 = -8(5^2) - 3(5) + 2 = -8(25) - 3(5) + 2 = -200 - 15 + 2 = -213
\]

Now we can summarize the first five terms of the sequence:
- \( a_1 = -9 \)
- \( a_2 = -36 \)
- \( a_3 = -79 \)
- \( a_4 = -138 \)
- \( a_5 = -213 \)

Thus, the first five terms of the sequence are:
\[
-9, -36, -79, -138, -213
\]