Use the rule for the 𝑛th term of an arithmetic sequence.  𝑡𝑛 = 𝑡1 + (𝑛 − 1)𝑑 where 𝑡𝑛 is 𝑛th term, 𝑡1 is first term, 𝑛 is term number and 𝑑 is common difference

A savings account begins with a deposit of $\$500$. Each month, an additional $\$75$ is deposited. Determine which expression represents the amount in the account at the start of month $n$.

A parking lot initially has 8 vehicles on Day 1. Each subsequent day, 5 more vehicles are added to the lot. (a) State the first term and the common difference. (b) Use the arithmetic sequence rule to calculate the number of vehicles in the lot on Day 15.

A fitness app tracks the total distance a runner has covered in training sessions over several weeks. Use the arithmetic sequence to determine the total distance in kilometres the runner will have covered by Week 28.

A savings account begins with an initial deposit of $\$500$. Each week, an additional $\$45$ is deposited. (a) Identify the first term and common difference of the resulting arithmetic sequence. (1 mark) (b) Use the arithmetic sequence rule to find the amount in the account after 16 weeks of deposits. (2 marks)

A wildlife reserve is introducing a breeding programme for endangered wallabies. In the first month, there are 24 wallabies. The population is expected to increase by 7 wallabies each month. (a) Find the common difference $d$. (1 mark) (b) Calculate the population in month 12. (2 marks)

A library introduces a new reading incentive program. The table shows the total number of books read by participants during the first four weeks of the program. Use the arithmetic sequence to determine the total number of books that will have been read 18 weeks after the program begins.