Explanation:
an arithmetic sequence means that every term of the sequence is created by adding a constant number to the previous term.
formally :
an = an-1 + d
so, in the sequence of
3, x, 12
we therefore know
x = 3 + d
12 = x + d = (3 + d) + d = 3 + 2d
9 = 2d
d = 9/2 = 4.5
the sequence is therefore
3, 7.5, 12
as
3 + 4.5 = 7.5
7.5 + 4.5 = 12
so, we are correct.