Answer:
[tex]a_{n}[/tex] = 100n - 112
Step-by-step explanation:
Given the recursive formula
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 100 with a₁ = - 12
This tells us that any term is found by adding 100 to the previous term
That is common difference d = 100 and a₁ = - 12
The explicit formula for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d , thus
[tex]a_{n}[/tex] = - 12 + 100(n - 1) = - 12 + 100n - 100 = 100n - 112
