Answer:
[tex]a_{n}[/tex] = 5n - 2
Step-by-step explanation:
The nth 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 a₄ = 18 , then
a₁ + 3d = 18 , that is
3 + 3d = 18 ( subtract 3 from both sides )
3d = 15 (divide both sides by 3 )
d = 5
Then
[tex]a_{n}[/tex] = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2 ← explicit rule
