5. A company that owned a silver mine
- extracted 480 tonnes of silver from the mine in year 1
- extracted 465 tonnes of silver from the mine in year 2
- extracted 450 tonnes of silver from the mine in year 3
and so on, forming an arithmetic sequence.
- Find the mass of silver extracted in year 14
After a total of 7770 tonnes of silver was extracted, the company stopped mining.
Given that this occurred at the end of year \(N\),
show that
$$N ^ { 2 } - 65 N + 1036 = 0$$Hence, state the value of \(N\).