A company producing salt from sea water changed to a new process. The amount of salt obtained each week increased by 2% of the amount obtained in the preceding week. It is given that in the first week after the change the company obtained 8000 kg of salt.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [B1] (i) r = 1.02 or 102/100 used in a GP in some way. Can be awarded here for use in Sn formula.
2. [M1] (i) Use of ar^(n-1) with a = 8000 & n = 12 or with a = 8000/1.02 and n = 13.
3. [A1] (i) Amount in 12th week = 8000(1.02)¹¹ = 9950 (kg) awrt. Note: Final answer of either 9943 or 9940 implies M1. Full marks can be awarded for a correct answer from a list of terms.
4. [M1] (ii) Use of Sn with a = 8000 and n = 12 or addition of 12 terms. Total is 8000((their r)¹² - 1) / ((their r) - 1).
5. [A1] (ii) = 107000 (kg) awrt. Correct answer but no working 2/2.