To create the arithmetic sequence [tex]\(a_n\)[/tex] using the given functions [tex]\(f(n) = 25\)[/tex] and [tex]\(g(n) = 3(n-1)\)[/tex], we start by combining these functions.
1. Define the arithmetic sequence:
[tex]\[
a_n = f(n) + g(n)
\][/tex]
2. Insert the given functions into the equation:
[tex]\[
a_n = 25 + 3(n-1)
\][/tex]
3. Simplify the expression:
[tex]\[
a_n = 25 + 3n - 3
\][/tex]
[tex]\[
a_n = 3n + 22
\][/tex]
Now that we have the expression for the arithmetic sequence [tex]\(a_n\)[/tex], we need to solve for the 12th term, i.e., [tex]\(a_{12}\)[/tex].
4. Substitute [tex]\(n = 12\)[/tex] into the sequence:
[tex]\[
a_{12} = 3(12) + 22
\][/tex]
5. Calculate the term:
[tex]\[
a_{12} = 36 + 22
\][/tex]
[tex]\[
a_{12} = 58
\][/tex]
Therefore, the 12th term of the arithmetic sequence [tex]\(a_n\)[/tex] is [tex]\(58\)[/tex].
