1. The problem is to find the number of terms in the finite arithmetic sequence: 16, 11, 6, 1, ..., -239. 2. The formula for the $n$-th term of an arithmetic sequence is: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term, $d$ is the common difference, and $a_n$ is the $n$-th term. 3. Identify the first term and common difference: - $a_1 = 16$ - $d = 11 - 16 = -5$ 4. We know the last term $a_n = -239$. Substitute into the formula: $$-239 = 16 + (n-1)(-5)$$ 5. Simplify and solve for $n$: $$-239 = 16 - 5(n-1)$$ $$-239 - 16 = -5(n-1)$$ $$-255 = -5(n-1)$$ $$\frac{-255}{-5} = n-1$$ $$51 = n-1$$ $$n = 52$$ 6. Therefore, the number of terms in the sequence is $\boxed{52}$.