1. **Problem Statement:** Calculate the projected expenditure of a company in 5 years if the current expenses are 34000 and they increase by 7.5% per year. 2. **Identify the type of sequence:** The expenditures form a geometric sequence because they increase by a fixed percentage each year. 3. **Define variables:** - Initial expenditure (first term) $a = 34000$ - Common ratio $r = 1 + \frac{7.5}{100} = 1.075$ - Number of years $n = 5$ 4. **Formula:** The expenditure after $n$ years is given by the $n$th term of the geometric sequence: $$ a_n = a \times r^n $$ 5. **Calculate:** $$ a_5 = 34000 \times (1.075)^5 $$ Calculate $(1.075)^5$: $$ (1.075)^5 \approx 1.4310 $$ So, $$ a_5 = 34000 \times 1.4310 = 48654 $$ 6. **Round to the nearest rand:** Projected expenditure after 5 years is approximately $48654$.