Continued from the previous question.Write down an expression for the amount of petrol in the tank, An, at the start of the nth minute. (Write your answer in the form a + bn)

Question

BlackTom AI · Accepted Answer

Arithmetic sequence model: the amounts form an arithmetic progression with common difference 750 litres per minute. The general term for an arithmetic sequence is A_n = A_1 + (n − 1)d, where A_1 is the amount at the start of the 1st minute and d is the change each minute.

1. Relevant concepts
- Arithmetic sequence formula A_n = A_1 + (n − 1)d.
- d = 750 (the tank gains 750 litres each minute).
- From the previous part (implied), A_1 = 1500 litres (the amount at the start of minute 1).

2. Step-by-step reasoning
- Substitute A_1 = 1500 and d = 750 into the formula:
  A_n = 1500 + (n − 1) × 750.

3. Calculations (showing intermediate steps)
- Multiply out: (n − 1) × 750 = 750n − 750.
- Add to 1500: A_n = 1500 + 750n − 750.
- Combine constants: 1500 − 750 = 750.
- Final simplified form: A_n = 750 + 750n.

4. Why this answer is correct
- This expression matches the arithmetic formula and the given initial value and rate of change.
- Check with small n: for n = 1, A_1 = 750 + 750(1) = 1500 (matches the stated start value). For n = 2, A_2 = 750 + 1500 = 2250, which equals 1500 + 750, showing a 750-litre increase per minute.

5. Why other plausible forms are incorrect
- 1500 + 750n would give A_1 = 2250, which contradicts the known A_1 = 1500.
- 750n gives A_1 = 750, which is too small.
- 1500 + 750(n − 1) is correct but simplifies to 750 + 750n; any unsimplified or mis-signed variants (e.g., 1500 − 750(n − 1)) would imply wrong direction or magnitude of change.

6. Conclusion
The amount of petrol at the start of the nth minute is A_n = 750 + 750n, which matches the provided answer.

Continued from the previous question.Write down an expression for the amount of petrol in the tank, An, at the start of the nth minute. (Write your answer in the form a + bn)Short answer

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