How do you write the iterative definition for a given sequence. for example {7, 5, 3, 1, -1 }

The process is also known as recurssion which is most often the term used in computer science.

Both terms mean that you do something to the previous term to get to the next term. In general terms it is written like this

fn = f_(n - 1) + d for an arithmetic progression. The series begins with n =2 , 3 , 4 , 5 , 6 ...
f1 is defined as 7

so f2 = f_(2 - 1) - 2 or
f2 = f_1 - 2
f2 = 7 - 2
f2 = 5

f3 = f_(3 - 1) - 2 or
f3 = f_2 - 2
f3 = 5 - 2
f3 = 3 and so on. Computers handle this much better than people do. They can go through a thousand such calculations most of the time in less than a second.