Answer:
You know that the beginning salary is $32,000, and it is raised by $1,000 per year.
a) We want to find a recursive relation, let's try to find a pattern:
S₁ = salary on the first year = $32,000
S₂ = salary on the second year = $32,000 + $1,000 = $33,000
S₃ = salary on the third year = $33,000 + $1,000 = $34,000
and so on.
We already can see that the recursive relation is: "the salary of the previous year plus $1,000", this can be written as:
Sₙ = Sₙ₋₁ + $1,000
Such that S₁ = $32,000
b) Your salary in the fifth year is S₅
Let's construct it:
S₃ = $34,000
S₄ = $34,000 + $1,000 = $35,000
S₅ = $35,000 + $1,000 = $36,000
Your salary on the fifth year is $36,000
c) When we have a recursive relation like:
Aₙ = Aₙ₋₁ + d
The sum of the first N elements is given by:
Sum(N) = N*(2*A₁ + (N - 1)*d)/2
Then the sum of your salary for the first 20 years is:
S(20) = 20*(2*$32,000 + (20 - 1)*$1,000)/2
S(20) = $830,000
