1. The problem asks to write the equation for the sequence 500, 2000, 3500, ... in "first term" form. 2. The "first term" form of an arithmetic sequence is given by the formula: $$t(n) = a + d(n - 1)$$ where $a$ is the first term and $d$ is the common difference. 3. Identify the first term $a$: The first term is $500$. 4. Find the common difference $d$: Calculate the difference between consecutive terms: $$2000 - 500 = 1500$$ $$3500 - 2000 = 1500$$ So, $d = 1500$. 5. Substitute $a = 500$ and $d = 1500$ into the formula: $$t(n) = 500 + 1500(n - 1)$$ 6. This is the equation for the sequence in "first term" form. Final answer: $$t(n) = 500 + 1500(n - 1)$$