Answer:
[tex]a_{n}[/tex] = [tex]\frac{1}{2}[/tex] n + 15
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₆ = 18 and d = [tex]\frac{1}{2}[/tex] , then
a₁ + 5d = 18 , that is
a₁ + [tex]\frac{5}{2}[/tex] = 18 ( subtract [tex]\frac{5}{2}[/tex] from both sides )
a₁ = [tex]\frac{31}{2}[/tex]
Thus
[tex]a_{n}[/tex] = [tex]\frac{31}{2}[/tex] + [tex]\frac{1}{2}[/tex] (n - 1) = [tex]\frac{15}{2}[/tex] + [tex]\frac{1}{2}[/tex] n - [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] n + 15
