What is the 52nd term of the sequence below?

-38 - 35 - 32 and - 29

And how did you get that answer

Because the difference between any term and the previous term is a constant, this is an arithmetic sequence because of that constant which is referred to as the common difference, d. Which in this case is - 35--38=-32--35=3

Any arithmetic sequence can be expressed as:

a (n) = a+d (n-1), a=initial term, d=common difference, n=term number.

In this case a=-38 and d=3 so

a (n) = - 38+3 (n-1) which we can simplify to

a (n) = - 38+3n-3

a (n) = 3n-41, so the 52nd term is:

a (52) = 3 (52) - 41

a (52) = 156-41

a (52) = 115