In a tower, the first floor has (4) windows and each next floor has (4) more windows. How many windows are there in (8) floors?
Answer and explanation
Correct answer: 144
The numbers of windows form an AP: 4, 8, 12, ..., where the first term is a = 4, common difference d = 4, and n = 8. The eighth floor has 4 + 7 × 4 = 32 windows. Therefore, S₈ = 8/2 × (4 + 32) = 144 windows. The value 136 would result from incorrectly taking the last term as 30. Exam tip: For AP sum questions, first find the nth term and then use Sₙ = n/2(a + l).
Frequently asked questions
What is the correct answer to this question?
144
Why is this the correct answer?
The numbers of windows form an AP: 4, 8, 12, ..., where the first term is a = 4, common difference d = 4, and n = 8. The eighth floor has 4 + 7 × 4 = 32 windows. Therefore, S₈ = 8/2 × (4 + 32) = 144 windows. The value 136 would result from incorrectly taking the last term as 30. Exam tip: For AP sum questions, first find the nth term and then use Sₙ = n/2(a + l).
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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