An arithmetic sequence (a_n) is as follows:

where

is the first term and d is the constant difference,
thus, we see that the n'th term of an arithmetic sequence is

in our particular case d=5, the third term is 8, so we have:

and the general term is

,
Answer: first term is -2, n'th term is -2+5(n-1)
125 > 50 + 4.25*p
subtract 50 from each side
75 =>4.25p
divide by 4.25
p>17.64
He may invite up to 17 people ( if he doesn't have to pay for himself)
He may invite 16 if he has to pay for himself