Respuesta :
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula
[tex]a_n = ar^{n-1}[/tex]
1) [tex]a_n = 50000(1.05)^{n-1}[/tex]
2) In order to find salary in 5 years we need to plug n=5, we get
[tex]a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4[/tex]
= 50000(1.21550625)
=$60775.3125.
3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.
[tex]S_n = \frac{a(1-r^n}{1-r}[/tex]
Plugging n=10, a = 50000 and r= 1.05.
[tex]S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}[/tex]
[tex]S_10 = \frac{50000(0.050)^{10}}{0.05}[/tex]
= 628894.62678.
