In a building the first floor has 180 windows and each next floor has 15 fewer windows. Which floor will have 45 windows?

Correct answer: 10

This problem uses the nth-term formula for a decreasing arithmetic progression. The first term is a = 180 because the first floor has 180 windows. Since every higher floor has 15 fewer windows, the common difference is d = −15. For the nth floor, aₙ = a + (n − 1)d. Put aₙ = 45: 45 = 180 + (n − 1)(−15). Hence −135 = −15(n − 1), so n − 1 = 9 and n = 10. Thus option C is correct. A direct check gives 180 on floor 1, 165 on floor 2, and after nine decreases, 180 − 9×15 = 45 on floor 10. Floor 8 has 75, floor 9 has 60, and floor 11 has 30 windows, so the distractors do not meet the requirement.