The first row of a hall has 36 seats and each next row has 6 more seats. If the total number of seats is 1566, how many rows are there?
Answer and explanation
Correct answer: 18
The seat counts form an arithmetic progression with first term a = 36 and common difference d = 6. If there are n rows, the total is S_n = n/2[2a + (n - 1)d]. Substitution gives 1566 = n/2[72 + 6(n - 1)] = n/2(6n + 66) = 3n(n + 11). Hence n(n + 11) = 522. Testing the positive whole-number choices, n = 18 gives 18 × 29 = 522, so the number of rows is 18. Option D is correct. The other choices do not produce the stated total when inserted into the sum formula.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The seat counts form an arithmetic progression with first term a = 36 and common difference d = 6. If there are n rows, the total is S_n = n/2[2a + (n - 1)d]. Substitution gives 1566 = n/2[72 + 6(n - 1)] = n/2(6n + 66) = 3n(n + 11). Hence n(n + 11) = 522. Testing the positive whole-number choices, n = 18 gives 18 × 29 = 522, so the number of rows is 18. Option D is correct. The other choices do not produce the stated total when inserted into the sum formula.
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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