I would love to stay and help you, but something has just come to my attention. Here is an example that I worked out for you, okay?
Arithmetic sequences allow you to predict the next number in a sequence by defining the pattern. If that doesn't make sense, I can give an example in a random sequence:
2, 6, 14,
Here's the equation for this sequence:
a_n +1 = 2a_n + 2
a_2 = 2(2) + 2; which equals 6. That's the second term.
a_3 = 2(6) + 2; which equals 14. That's the third term.
As you can see, you ALWAYS add the number you got from the previous equation to the next equation.
This same thing can be applied to your question, okay?
we know that a_n + 3 = the amount of seats in the room (or S)
For the first row, we could look at it like this:
a_n + 3 = 18
If you finish this equation you'll find that a_n = 15. :)