We are given the recursive formula:

$a_n = a_{n-1} + 5$ with the initial condition $a_1 = -16$.

To find $a_{73}$:

This is an arithmetic sequence because the difference between consecutive terms is constant, specifically $d = 5$. The general formula for the $n$-th term of an arithmetic sequence is:

$a_n = a_1 + (n - 1) \cdot d$

Substituting the given values:

$a_{73} = a_1 + (73 - 1) \cdot 5$ $a_{73} = -16 + 72 \cdot 5$ $a_{73} = -16 + 360$ $a_{73} = 344$

Thus, $a_{73} = 344$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the general term formula for an arithmetic sequence?
2. How do you find the sum of an arithmetic sequence?
3. What would the 100th term $a_{100}$ be for this sequence?
4. How can you derive the recursive formula from the general formula of an arithmetic sequence?
5. What is the difference between recursive and explicit formulas?

Tip: In an arithmetic sequence, the recursive formula gives the relationship between consecutive terms, while the explicit formula directly calculates any term.