Luke earned 36,000 during the first year of his job at putt putt Kingdom. After each year he received a 10% raise find his total earnings during the first five years of the job.
Each year Luke earns the amount earned the previous year multiplied by 1.10 (which corresponds to a 10% raise). The total earnings will be the sum of each year earnings. This sum is given by the geometric series formula: [tex] S_{n} = \frac{ a_{1}(1 - r^{n}) }{1 - r} [/tex]
where: a₁ = first term of the series r = common ratio n = number of term wanted
Therefore, the total earnings will be: [tex] S_{n} = \frac{ 36000(1 - 1.10^{5}) }{1 - 1.10} [/tex] = 219783.60$
During the first five years of the job Luke earned219783.60$.
