A staircase has (132) tiles in the bottom row and (6) fewer tiles in each upper row. Which row will have (54) tiles?

Correct answer: 14th row

The number of tiles forms a decreasing AP from the bottom row, with first term \(a=132\) and common difference \(d=-6\). Thus, the number of tiles in the \(n\)th row is \(a_n=132+(n-1)(-6)\). Using \(132-6(n-1)=54\), we get \(6(n-1)=78\), so \(n-1=13\) and \(n=14\). Therefore, the 14th row has 54 tiles. The 13th row has 60 tiles, so it is a close but incorrect option. Exam tip: use a negative common difference for a decreasing AP.