Net-Zero Buses

15 cities, each of varying sizes, decide to have carbon-neutral public transport systems.

When the cities are arranged in size order from smallest to largest, the number of new electric buses they need follows an arithmetic sequence with first term (representing the smallest amount of buses needed for the smallest city) a buses and common difference d buses. 

The 7ᵗʰ city in this progression needs 580 new electric buses and the largest city needs 1020 new electric buses.

Find the value of a and the value of d.

[5 marks]

EV Increase

A country decides to subsidise the purchase of electric vehicles, causing more people to buy them.

Initially, the country used an equivalent of 56 million tonnes of oil for transport.

Since the government subsidy, the transport sector in each subsequent year has required 80% of the amount of oil that the previous year required.


a) Write a recurrence relation to model the amount of oil used, in million tonnes, in each subsequent year.

[2 marks]

b) Find the amount of oil needed for the transport sector after the fifth year.

[2 marks]

c) Find the total amount of oil used until the transport sector requires no more oil.

[4 marks]

d) State one limitation with the model.

[1 mark]