Any arithmetic sequence can be expressed as:
a(n)=a+d(n-1), a=initial term, d=common difference, n=term number
We are only told that d=5 and a(12)=63 so:
53=a+5(12-1)
53=a+60-5
53=a+55
a=-2 now we have solved for a and we can say:
a(n)=-2+5(n-1) which neatened up....
a(n)=-2+5n-5
a(n)=5n-7
The above is the rule to find the value of the nth term.