Let x+500 represent the first year
For the $500 more than the previous year for 4 years, we would write:
(x+500)+(x+500+500+500)+(x+500+500+500+500)= 17,800
By adding the equation above, 4x+5000=17,800
4x=17,800-5000
4x=12,800
x=3,200
So the amount the man was paid in the first year is 3,200+500=3,700