Aconcession stand vendor counts the money in the register. after 2 h, it has $82.75. after 6 h, it has $360.75. how much money will be in the register at the end of an 8-hour shift?

We've got an algebraic sequence. Let's solve it!
First, we'll subtract the initial amount (at 2 hours) from the amount at 6:
360.75 - 82.75 = 278
Now we divide by what number in the sequence it is minus one (It's the 5th term, so we'll do 278/4)
278/4 = 69.5
82.75 - 69.5 = 13.25
Now that we've got that, let's create the equation:
an = 13.25 + 69.5(x-1)
Plug in 8:
13.25 + 69.5(8-1) = 499.75

There will be $499.75 in the register at the end of the 8-hour shift.