In a parking arrangement, the \(r\)th row has \(5r\) vehicles. How many vehicles are there in 42 rows?
Answer and explanation
Correct answer: 4515
The number of vehicles in row \(r\) is \(5r\), so the total for 42 rows is \(5(1+2+\cdots+42)=5S_{42}\). Apply \(S_n=\frac{n(n+1)}2\): \(S_{42}=\frac{42\cdot43}{2}=21\cdot43=903\). Hence the total number of vehicles is \(5\cdot903=4515\), which is option C. The factor 5 must be retained for every row; it can be taken outside the sum because it is common. Options A, B, and D do not equal five times the sum of the first 42 natural numbers and therefore do not represent the stated arrangement.
Frequently asked questions
What is the correct answer to this question?
4515
Why is this the correct answer?
The number of vehicles in row \(r\) is \(5r\), so the total for 42 rows is \(5(1+2+\cdots+42)=5S_{42}\). Apply \(S_n=\frac{n(n+1)}2\): \(S_{42}=\frac{42\cdot43}{2}=21\cdot43=903\). Hence the total number of vehicles is \(5\cdot903=4515\), which is option C. The factor 5 must be retained for every row; it can be taken outside the sum because it is common. Options A, B, and D do not equal five times the sum of the first 42 natural numbers and therefore do not represent the stated arrangement.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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