In a building, the first floor has 220 windows and each successive floor has 20 fewer windows. Which floor will have 40 windows?
Answer and explanation
Correct answer: 10
The numbers of windows form an arithmetic progression with first term a = 220 and common difference d = −20, because the number decreases by 20 on each successive floor. The nth-term formula is aₙ = a + (n − 1)d. Substituting the required number 40 gives 40 = 220 + (n − 1)(−20). Hence, −180 = −20(n − 1), so n − 1 = 9 and n = 10. Therefore, the tenth floor has 40 windows, making option C correct. Checking the sequence confirms this: floor 1 has 220 windows, floor 2 has 200, and after nine decreases of 20, floor 10 has 40. The other choices correspond to 60, 80 or 20 windows.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The numbers of windows form an arithmetic progression with first term a = 220 and common difference d = −20, because the number decreases by 20 on each successive floor. The nth-term formula is aₙ = a + (n − 1)d. Substituting the required number 40 gives 40 = 220 + (n − 1)(−20). Hence, −180 = −20(n − 1), so n − 1 = 9 and n = 10. Therefore, the tenth floor has 40 windows, making option C correct. Checking the sequence confirms this: floor 1 has 220 windows, floor 2 has 200, and after nine decreases of 20, floor 10 has 40. The other choices correspond to 60, 80 or 20 windows.
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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