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In a building the first floor has 150 windows and each next floor has 10 fewer windows. Which floor will have 60 windows?

Answer and explanation

Correct answer: 10

This is an arithmetic-progression word problem involving the nth term. The first-floor count is the first term, a = 150, and the number of windows decreases by 10 on every successive floor, so the common difference is d = −10. For the nth floor, use aₙ = a + (n − 1)d. Setting the required count equal to 60 gives 60 = 150 + (n − 1)(−10). Thus −90 = −10(n − 1), so n − 1 = 9 and n = 10. Therefore, option C is correct. The sequence is 150, 140, 130, 120, 110, 100, 90, 80, 70, 60. Option A would give 80 windows, option B 70, and option D 50, so none of them satisfies the condition.

Related tags

Arithmetic ProgressionNth TermDecreasing SequenceWord ProblemsClass 10 MathematicsWord Problems Based On ApsArithmetic Progressions (Ap)Arithmetic Progressions Ap

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