Question

Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1. an = –6n2 − 5n + 4 , , ,

Answer 1

To find the first four terms of the sequence given by the formula \( a_n = -6n^2 - 5n + 4 \), we can compute the values for \( n = 1, 2, 3, \) and \( 4 \).

1. For \( n = 1 \):
\[
a_1 = -6(1^2) - 5(1) + 4 = -6(1) - 5 + 4 = -6 - 5 + 4 = -7
\]

2. For \( n = 2 \):
\[
a_2 = -6(2^2) - 5(2) + 4 = -6(4) - 10 + 4 = -24 - 10 + 4 = -30
\]

3. For \( n = 3 \):
\[
a_3 = -6(3^2) - 5(3) + 4 = -6(9) - 15 + 4 = -54 - 15 + 4 = -65
\]

4. For \( n = 4 \):
\[
a_4 = -6(4^2) - 5(4) + 4 = -6(16) - 20 + 4 = -96 - 20 + 4 = -112
\]

Now we can list out the first four terms of the sequence:
- \( a_1 = -7 \)
- \( a_2 = -30 \)
- \( a_3 = -65 \)
- \( a_4 = -112 \)

So, the first four terms are:
\[
-7, -30, -65, -112
\]