In a building the first floor has 180 windows and each next floor has 15 fewer windows. Which floor will have 45 windows?
Answer and explanation
Correct answer: 10
This problem uses the nth-term formula for a decreasing arithmetic progression. The first term is a = 180 and the common difference is d = −15 because every higher floor has 15 fewer windows. Set the nth term equal to 45: 45 = 180 + (n−1)(−15). This gives −135 = −15(n−1), so n−1 = 9 and n = 10. The sequence confirms the result: the first floor has 180 windows, the second 165, and after nine decreases the tenth floor has 45. Hence option C is correct. Options A, B and D give 75, 60 and 30 windows respectively.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
This problem uses the nth-term formula for a decreasing arithmetic progression. The first term is a = 180 and the common difference is d = −15 because every higher floor has 15 fewer windows. Set the nth term equal to 45: 45 = 180 + (n−1)(−15). This gives −135 = −15(n−1), so n−1 = 9 and n = 10. The sequence confirms the result: the first floor has 180 windows, the second 165, and after nine decreases the tenth floor has 45. Hence option C is correct. Options A, B and D give 75, 60 and 30 windows respectively.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
