To find the 20th term of the arithmetic sequence [tex]\(-8, -7, -6, -5, \ldots\)[/tex], let us identify the relevant components of the sequence and apply the formula for the [tex]\(n\)[/tex]-th term of an arithmetic sequence.
An arithmetic sequence is defined by its first term [tex]\(a_1\)[/tex] and the common difference [tex]\(d\)[/tex]. For the given sequence:
- The first term [tex]\(a_1\)[/tex] is [tex]\(-8\)[/tex].
- The common difference [tex]\(d\)[/tex] is calculated by subtracting the first term from the second term. In this case, [tex]\(d = -7 - (-8) = 1\)[/tex].
The formula for the [tex]\(n\)[/tex]-th term ([tex]\(a_n\)[/tex]) of an arithmetic sequence is given by:
[tex]\[
a_n = a_1 + (n - 1) \cdot d
\][/tex]
To find the 20th term ([tex]\(a_{20}\)[/tex]), we plug in [tex]\(n = 20\)[/tex], [tex]\(a_1 = -8\)[/tex], and [tex]\(d = 1\)[/tex] into the formula:
[tex]\[
a_{20} = -8 + (20 - 1) \cdot 1
\][/tex]
Now, calculate the expression inside the parentheses first:
[tex]\[
20 - 1 = 19
\][/tex]
Then, multiply this result by the common difference [tex]\(d\)[/tex]:
[tex]\[
19 \cdot 1 = 19
\][/tex]
Finally, add this result to the first term [tex]\(a_1\)[/tex]:
[tex]\[
-8 + 19 = 11
\][/tex]
Therefore, the 20th term of the arithmetic sequence is [tex]\(\boxed{11}\)[/tex]. Thus, option [tex]\(a. a_{20} = 11\)[/tex] is correct.
