Answer:
(a) The required recurrence relation for the salary of the employee of n years after 2009 is
.
(b)The salary of the employee will be $83421.88 in 2017.
(c) 
Step-by-step explanation:
Summation of a G.P series
(a)
Every year the salary is increasing 5% of the salary of the previous year plus $1000.
Let
represents the salary of the employee of n years after 2009.
Then
represents the salary of the employee of (n-1) years after 2009.
Then 



The required recurrence relation for the salary of the employee of n years after 2009 is
.
(b)
Given, 

Since 2017 is 8 years after 2009.
So, n=8.
∴ 



















≈$83421.88
The salary of the employee will be $83421.88 in 2017.
(c)
Given, 

We successively apply the recurrence relation






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