Determine the number of terms n in the arithmetic sequence.

a1 = 9, an = 72, Sn = 405

I'm a little confused on the question, or it just may be I'm not smart enough to understand..

It has nothing to do with intelligence, most likely you have not learned it yet.

It is a topic called sequences and series.

Let me see.

AP

a=9

Tn=a+(n-1)d = 72

so

9+(n-1)d=72

Sn=n/2(a+Tn) = 405

n/2 * (9+72) =405

n/2 * 81 = 405

n=10