1. **State the problem:** Randy colors squares in a repeating sequence of 5 colors: green, red, blue, pink, purple. 2. **Goal:** Find the color of the 2017th square. 3. **Method:** Since the colors repeat every 5 squares, we use modular arithmetic to find the position of the 2017th square in the cycle. 4. **Formula:** The position in the cycle is given by $$2017 \mod 5$$. 5. **Calculate:** $$2017 \div 5 = 403 \text{ remainder } 2$$ 6. **Interpret remainder:** - Remainder 1 corresponds to green (1st color) - Remainder 2 corresponds to red (2nd color) - Remainder 3 corresponds to blue (3rd color) - Remainder 4 corresponds to pink (4th color) - Remainder 0 corresponds to purple (5th color) 7. Since the remainder is 2, the 2017th square is colored **red**. **Final answer:** (b) Red