Edexcel IAL WMA12/01/P2/Oct 2021/Q5 (Arithmetic Sequences & Series, Modelling)
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
(2)
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
(3)
Hence, state the value of N.
(1)
SOLUTION
a- Since the company’s extraction forms the arithmetic sequence, to find the mass extracted in year 14, use the nth term formula of arithmetic sequence.
Where,
Hence, in 14th years, 285 tonnes of silver were extracted.
b- It can be simply written that the by N years, the total or sum of silver extracted was 7770 tonnes. Therefore applying the summation of n terms formula of arithmetic series. Where,
Using the first formula from the flashcard.
c- To find the value of N, lets solve the quadratic equation.
Applying the quadratic formula, where
We will accept 28, for it is given that the company stopped mining after 7770 tonnes of silver was extracted. Hence, by the solution of quadratic equation this is possible when either N is 28 or 37. So we will accept the first possible value that is 28.
