Remark
The formula for this series is
t_n = n^2 - 1
Step-by-step explanation
If the series ends at 288, then the highest value n can have is 17
So you would write t_n = n^2 - 1 n
If you said this to someone, you would say "t_n = n squared minus 1 where n is such that 1 is greater than or equal to 1 or less than or equal to 17"
Example
What is the 4th term in this series?
t_4 = 4^2 - 1
t_4 = 16 - 1
t_4 = 15