Question

Thirty six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter, after the second car, there are two scooters, after the third car, there are three scooters and so on. Work out the number of scooters in the second half of the row.

• A. 17
• B. 15
• C. 12
• D. 10

Hint:

For problems involving arithmetic progressions, break the sequence into parts and use the sum formula to find the total number of terms. This helps simplify the process.

Answer 1

The Correct Option is B

There are 36 vehicles in total. The sequence of scooters after each car is: - After the first car: 1 scooter
- After the second car: 2 scooters
- After the third car: 3 scooters
- And so on.
This forms an arithmetic progression where the first term is 1, and the common difference is 1.
The second half of the row consists of 18 vehicles, from the 19th vehicle to the 36th vehicle. We need to calculate the number of scooters in this section of the row.
The number of scooters in the second half forms an arithmetic sequence starting from the 19th vehicle. The sum of the first \(n\) integers is given by the formula: \[ S_n = \frac{n(n+1)}{2}. \] For the first 18 terms (from the 19th to the 36th vehicle): \[ S_{18} = \frac{18 \times 19}{2} = 171. \] Thus, the total number of scooters in the second half is 15.