1. The problem gives the arithmetic series: $$3 + 8 + 13 + \dots + 218 + 223$$ and asks to express the general term $$a_k$$ in terms of $$k$$ and find the number of terms $$n$$. 2. This is an arithmetic sequence where each term increases by a constant difference. The first term $$a_1 = 3$$ and the common difference $$d = 8 - 3 = 5$$. 3. The formula for the $$k$$-th term of an arithmetic sequence is: $$a_k = a_1 + (k-1)d$$ 4. Substitute the known values: $$a_k = 3 + (k-1)5 = 3 + 5k - 5 = 5k - 2$$ 5. To find $$n$$, use the last term given $$a_n = 223$$: $$223 = 5n - 2$$ 6. Solve for $$n$$: $$5n = 223 + 2 = 225$$ $$n = \frac{225}{5} = 45$$ 7. Therefore, the general term is $$a_k = 5k - 2$$ and the number of terms is $$n = 45$$.