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Class 10MathematicsArithmetic Progressions (AP)Word problems based on APsHard
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A staircase has (110) tiles in the bottom row and (5) fewer tiles in each upper row. Which row will have (55) tiles?

Answer and explanation

Correct answer: 12th row

The numbers of tiles, counted from the bottom, form a decreasing AP with first term 110 and common difference -5. Thus, the number of tiles in the nth row is \(110+(n-1)(-5)\). Setting this equal to 55 gives \(110-5(n-1)=55\), so \(n-1=11\) and \(n=12\). Therefore, the 12th row has 55 tiles. The 11th row has 60 tiles, so it is a close but incorrect option. Exam tip: use a negative common difference when the terms decrease upwards.

Related tags

Arithmetic ProgressionAp Word ProblemsStaircase TilesDecreasing SequenceNth TermWord Problems Based On ApsArithmetic Progressions (Ap)Arithmetic Progressions Ap
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