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a An elevator in a tower is at a height of 7 m on the first floor. It rises to a height of 19 m when it reaches fourth floor. The lift moves up at a constant height every floor. The height of the lift at each floor forms an increasing linear sequence. What height is the lift at when it is on the second and third floors?

Ask by Gibbs Chandler. in Malaysia
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The elevator is at \(11 \, \text{m}\) on the second floor and \(15 \, \text{m}\) on the third floor.

Solution

We are given that the elevator is at \(7 \, \text{m}\) on the first floor and \(19 \, \text{m}\) on the fourth floor. Since the height increases linearly with each floor, the height forms an arithmetic sequence. 1. First, let the common difference be \( d \). In an arithmetic sequence, the \(n\)th term is given by: \[ a_n = a_1 + (n-1)d \] For the fourth floor (\(n = 4\)): \[ 19 = 7 + 3d \] 2. Solve for \( d \): \[ 19 - 7 = 3d \implies 12 = 3d \implies d = 4 \] 3. Now, determine the height on the second floor (\(n = 2\)): \[ a_2 = 7 + (2-1) \times 4 = 7 + 4 = 11 \] 4. Determine the height on the third floor (\(n = 3\)): \[ a_3 = 7 + (3-1) \times 4 = 7 + 8 = 15 \] Thus, the heights of the lift are: - Second floor: \(11 \, \text{m}\) - Third floor: \(15 \, \text{m}\)

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The Deep Dive

To find the height of the lift at the second and third floors, let’s first establish the height difference between the floors. The first floor is at 7 m, and the fourth floor is at 19 m. The height gained from the first to the fourth floor is 19 m - 7 m = 12 m. Since there are three intervals (1st to 2nd, 2nd to 3rd, and 3rd to 4th), the height gained per floor is 12 m / 3 = 4 m. Therefore, the height at the second floor is 7 m + 4 m = 11 m, and at the third floor, it is 11 m + 4 m = 15 m. So, the heights are 11 m for the second floor and 15 m for the third floor. The lift's movement is predictable! In fact, it’s almost like an escalator of numbers, gliding up through a neat 4-meter jump that makes you feel like you're ascending through stacked layers of a delicious cake, with each level cradling a delightful height that’s just waiting to be enjoyed. If you're wondering about similar systems, elevators are a great example of linear functions in real life. They make calculating heights in tall buildings straightforward, similar to how you’d tackle a simple math problem. Remember this key concept whenever you’re trying to find heights or distances that follow a consistent pattern – it can save you time and boost your confidence!

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