Sequences are part of the Year 12 Mathematics Applications course and sometimes it’s tricky to work out which terms the question requires.
For example, ATAR 2020 Question 11
Judith monitors the water quality in her garden pond at the same time everyday. She likes to maintain the concentration of algae between 200 and 250 unites per 100 litres (L). Her measurements show that the concentration increases daily according to the recursive rule
where
units per 100 L (the minimum concentration)
When the concentration gets above the 250 units per 100 L limit, she treats the water to bring the concentration back to the minimum 200 units per 100 l.
(a) If Judith treated the water on Sunday 6 December 2020, determine
(i) the concentration on Wednesday, 9 December 2020.
(ii) the day when she next treated the water.(b) During the first week of January 2021, Judith monitored the water and recorded the following readings
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Concentration (C) | 200 | 206 | 212.28 | 218.55 | 225.10 | 231.85 | 238.81 |
(i) Determine the revised recursive rule.
(ii) If she treated the water on 10 January and went on holiday until 20 January, when she next treated the water, calculate the concentration of the water on her return. Assuming the recursive rule from (b)(i) is used.
(a)(i) If  is the 6th of December, then what term is the 9th of January?I find most students simply do  so  , but this means they are off by one.It’s better to list them 6th 7th  8th 9th  Hence we want to find  The concentration on Wednesday 9 December is 215.38 units per 100 L a(ii) We need to find when the concentration is greater than 250   , what day is  ?The 9th is , 10th  , etc. 16th is Judith next treats the water on Wednesday 16 December (b) (i)   where (ii) is the 10th of January, 20th of January is   The concentration of the water on Judith’s return is 268.78 units per 100 L |
I get my students to count on their fingers to ensure they get the correct term or day.