In a building the first floor has (150) windows and each next floor has (7) fewer windows. Which floor will have (52) windows?
Answer and explanation
Correct answer: 15
The number of windows forms a decreasing AP with \(a=150\) and \(d=-7\). Thus, \(a_n=150+(n-1)(-7)\). Substituting \(a_n=52\) gives \(150-7(n-1)=52\), so \(7(n-1)=98\) and \(n=15\). The 14th floor would have 59 windows and the 16th floor would have 45, so the correct answer is the 15th floor. Exam tip: write the common difference as negative for a decreasing AP.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The number of windows forms a decreasing AP with \(a=150\) and \(d=-7\). Thus, \(a_n=150+(n-1)(-7)\). Substituting \(a_n=52\) gives \(150-7(n-1)=52\), so \(7(n-1)=98\) and \(n=15\). The 14th floor would have 59 windows and the 16th floor would have 45, so the correct answer is the 15th floor. Exam tip: write the common difference as negative for a decreasing AP.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
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