In a building, the first floor has 260 windows and each next floor has 18 fewer windows. Which floor will have 62 windows?
Answer and explanation
Correct answer: 12
The numbers of windows form an arithmetic progression with first term a = 260 and common difference d = −18, because the number decreases by 18 on every successive floor. For the nth floor, use a_n = a + (n − 1)d. Substituting the given number of windows gives 62 = 260 + (n − 1)(−18). Hence, 62 − 260 = −198, so n − 1 = 11 and n = 12. A quick check confirms the result: the twelfth floor has 260 − 11 × 18 = 260 − 198 = 62 windows. Therefore option C is correct; the other choices result from an incorrect step count or sign.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The numbers of windows form an arithmetic progression with first term a = 260 and common difference d = −18, because the number decreases by 18 on every successive floor. For the nth floor, use a_n = a + (n − 1)d. Substituting the given number of windows gives 62 = 260 + (n − 1)(−18). Hence, 62 − 260 = −198, so n − 1 = 11 and n = 12. A quick check confirms the result: the twelfth floor has 260 − 11 × 18 = 260 − 198 = 62 windows. Therefore option C is correct; the other choices result from an incorrect step count or sign.
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.
