In a triangular parking arrangement, the (1)st row has (2) vehicles, the (2)nd has (4) vehicles, and the (40)th has (80) vehicles. How many vehicles are there in total?
Answer and explanation
Correct answer: 1640
The numbers of vehicles in the rows are 2, 4, 6, ..., 80, so the number in each row is twice its row number. Hence the total is \(2(1+2+3+\cdots+40)\). Since \(1+2+\cdots+40=\frac{40\times41}{2}=820\), the total is \(2\times820=1640\) vehicles. The value 1600 may result from using \(40\times40\), but that is not the correct sum of this arithmetic progression. Exam tip: identify the first term, last term and number of terms, then use \(S_n=\frac{n}{2}(a+l)\).
Frequently asked questions
What is the correct answer to this question?
1640
Why is this the correct answer?
The numbers of vehicles in the rows are 2, 4, 6, ..., 80, so the number in each row is twice its row number. Hence the total is \(2(1+2+3+\cdots+40)\). Since \(1+2+\cdots+40=\frac{40\times41}{2}=820\), the total is \(2\times820=1640\) vehicles. The value 1600 may result from using \(40\times40\), but that is not the correct sum of this arithmetic progression. Exam tip: identify the first term, last term and number of terms, then use \(S_n=\frac{n}{2}(a+l)\).
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
