To find the first seven terms of the sequence given by the formula [tex]\( a_n = 12 - 3n \)[/tex], we need to substitute [tex]\( n \)[/tex] with values from 1 to 7. Here's a detailed step-by-step process:
1. First Term ([tex]\( n = 1 \)[/tex]):
[tex]\[
a_1 = 12 - 3 \cdot 1 = 12 - 3 = 9
\][/tex]
2. Second Term ([tex]\( n = 2 \)[/tex]):
[tex]\[
a_2 = 12 - 3 \cdot 2 = 12 - 6 = 6
\][/tex]
3. Third Term ([tex]\( n = 3 \)[/tex]):
[tex]\[
a_3 = 12 - 3 \cdot 3 = 12 - 9 = 3
\][/tex]
4. Fourth Term ([tex]\( n = 4 \)[/tex]):
[tex]\[
a_4 = 12 - 3 \cdot 4 = 12 - 12 = 0
\][/tex]
5. Fifth Term ([tex]\( n = 5 \)[/tex]):
[tex]\[
a_5 = 12 - 3 \cdot 5 = 12 - 15 = -3
\][/tex]
6. Sixth Term ([tex]\( n = 6 \)[/tex]):
[tex]\[
a_6 = 12 - 3 \cdot 6 = 12 - 18 = -6
\][/tex]
7. Seventh Term ([tex]\( n = 7 \)[/tex]):
[tex]\[
a_7 = 12 - 3 \cdot 7 = 12 - 21 = -9
\][/tex]
After calculating each term, we can list the first seven terms of the sequence as follows:
[tex]\[
[9, 6, 3, 0, -3, -6, -9]
\][/tex]
Thus, the first seven terms of the sequence [tex]\( a_n = 12 - 3n \)[/tex] are [tex]\( 9, 6, 3, 0, -3, -6, \)[/tex] and [tex]\( -9 \)[/tex].
