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