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Class 10MathematicsArithmetic Progressions (AP)Word problems based on APsHard
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A staircase has (80) tiles in the bottom row and (5) fewer tiles in each upper row. Which row will have (25) tiles?

Answer and explanation

Correct answer: 12th row

The numbers of tiles form a decreasing AP with first term \(a=80\) and common difference \(d=-5\). The number of tiles in the \(n\)th row is \(a_n=80+(n-1)(-5)\). From \(80-5(n-1)=25\), we get \(n-1=11\), so \(n=12\). Hence, the 12th row has 25 tiles. The 11th row has 30 tiles, so it is a close but incorrect option. Exam tip: use a negative common difference when quantities decrease.

Related tags

Arithmetic ProgressionsAp Word ProblemsNth TermDecreasing ApClass 10 MathematicsWord Problems Based On ApsArithmetic Progressions (Ap)Arithmetic Progressions Ap
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