Let's find the first three terms of the arithmetic sequence given by [tex]\( a_n = 11 - 3(n-1) \)[/tex].
1. First term ([tex]\( n = 1 \)[/tex]):
[tex]\[
a_1 = 11 - 3(1 - 1)
\][/tex]
Simplify the expression inside the parentheses first:
[tex]\[
a_1 = 11 - 3(0)
\][/tex]
Then perform the multiplication:
[tex]\[
a_1 = 11 - 0 = 11
\][/tex]
So, the first term is [tex]\( 11 \)[/tex].
2. Second term ([tex]\( n = 2 \)[/tex]):
[tex]\[
a_2 = 11 - 3(2 - 1)
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
a_2 = 11 - 3(1)
\][/tex]
Then perform the multiplication:
[tex]\[
a_2 = 11 - 3 = 8
\][/tex]
So, the second term is [tex]\( 8 \)[/tex].
3. Third term ([tex]\( n = 3 \)[/tex]):
[tex]\[
a_3 = 11 - 3(3 - 1)
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
a_3 = 11 - 3(2)
\][/tex]
Then perform the multiplication:
[tex]\[
a_3 = 11 - 6 = 5
\][/tex]
So, the third term is [tex]\( 5 \)[/tex].
Therefore, the first three terms of the arithmetic sequence are [tex]\( 11 \)[/tex], [tex]\( 8 \)[/tex], and [tex]\( 5 \)[/tex]. Among the given options, the correct answer is:
[tex]\[
\boxed{11, 8, 5}
\][/tex]
