Sequences & Series  Arithmetic  Applied & practical questions.
Test Yourself 1.
1. Sarah has recently begun her driving lessons so that she can obtain her licence after her exams in November of this year.
Her first lesson was 20 minutes, her second lesson was 30 minutes and each subsequent lesson was 10 minutes longer than the previous lesson. Hint.Be careful of the time units!!. Answer.2(i) 25^{th} lesson: 4 hours 20 min. (ii) Total  58 hours 20 mins. .(iii) During the 28th lesson. 
2. David is saving to buy a new car. He is planning to spend $16,000 on the car.
He already has $7,500 saved but now plans to save more seriously by putting more money aside from his wages. He begins by putting $100 aside in the first month. The next month he puts $150 aside and in the third month he puts $200 aside. Answer.(i) 17 more months. (ii) Saving $900. 
3. Ellen is being offered a Traineeship while she competes her University courses. She can elect to choose between two different salary packages.

4. A very tall building with 106 floors is to be constructed.
The first floor will be built at a cost of $3 million. Each subsequent floor will cost $0.5 million more than the previous floor. Answer.(i) Floor 42 cost $23.5 million. (ii) Total = $2,881.5 million. 
5. Damien and Alyssa are employed by an accounting firm.
By developing two sequences for their respective salaries, find in which year of employment Alyssa will be earning more that Damien? Hint.Be very careful how you interpret your answer.Answer.(i) Floor 42 cost $23.5 million. (ii) Total = $2,881.5 million. 
6. In the lead up to the swimming World Championships, one of the Australian swimmers was placed on a new training regime by his coach on returning from injury. On the first day, he had to complete 26 laps of the 50 m pool.
On each succeeding day, the laps to be completed increased by 6 (hence to 32 laps, 38 laps, etc) until 200 laps were being completed. At that stage, the swimmer had to maintain the 200 laps per day for another 14 days. Answer.(i) Day 30. (ii) Total = 309.5 km. 
7. A timber worker is stacking logs. The logs are stacked in layers so that each layer has 2 less logs than are stacked in the row below.
There are 8 logs in the top row, 10 in the next row and so on. There are n rows altogether. Answer.(i) No of logs = 6 + 2n. 
8. During an examination, the supervisor stands 3 metres in front of the first desk in a column of desks holding a box of tissues, Students are seated in columns of desks with 1 metre from the front of one desk to the front of the next desk. There are 25 desks in a column.
All 25 students in a particular column of desks take turns in asking for a tissue. Each student waits until the supervisor returns to the supervising position 3 metres in front of the first desk of the column, before putting their hand up and requesting a tissue. How many metres will the supervisor have to walk to provide each of the 25 students with one tissue and returning to the position 3 metres in front of the first desk? Answer.Distance = 750 m. 
9. Concrete blocks are used to build a wall to stop erosion. Each block is 1.5 m wide.
The lowest row (we will call it Row 1) is 180 m long. Each of the rows above the base row Above Row 20, each of the rows have 1 less block than the row below. That pattern continues until the top row which has a total of 10 blocks. Answer.(i) 120 blocks. (ii) 73 rows. (iii) 3,738 blocks. 
10. Susan is very fond of horses. She has a large paddock with a series of troughs into which she dumps a large bucket of hay for the horses. Susan walks from her truck, pours the hay into the trough and then walks back to her truck. She does that in turn for all the toughs in the paddock.
The first trough is 50 m from the gate where her truck is parked. The second trough is 50 m further and the other 8 troughs are also 50 m further apart. Answer.(i) 300 m. (ii) 1,000 m. (iii) Total distance = 5.5 km. 