Answer :
The first thing to know is that "an" and "a1" are names with subscripts and are and different from multiplication.
an = a1 + (n-1) d
add -a1 to both sides
an - a1 = a1 - a1 + (n-1) d
an - a1 = (n-1) d
d = (an-a1)/(n-1)
an = a1 + (n-1) d
add -a1 to both sides
an - a1 = a1 - a1 + (n-1) d
an - a1 = (n-1) d
d = (an-a1)/(n-1)