The other tutor's answer is wrong.


__, __, __, __, __, __, __, 25, __, __, __, __, __, __, __, __, __, __, __, -11, __, ...   

The general term of any arithmetic sequence is the formula
for the nth term which is

an = a1 + (n - 1)d

Substitute 8 for n:

a8 = a1 + (8 - 1)d

a8 = a1 + 7d

Substitute 25 for a8

25 = a1 + 7d

a1 + 7d = 25

----------------

an = a1 + (n - 1)d

Substitute 20 for n:

a20 = a1 + (20 - 1)d

a20 = a1 + 19d

Substitute -11 for a20

-11 = a1 + 19d

a1 + 19d = -11

Now we have the system of equations:

a1 +  7d =  25
a1 + 19d = -11

Solve the first one for a1
      a1 =  25 - 7d

Substitute (25 - 7d) for a1

(25 - 7d) + 19d = -11
  25 - 7d + 19d = -11
       25 + 12d = -11
            12d = -36
              d = -3

             a1 =  25 - 7d
             a1 =  25 - 7(-3)
             a1 =  25 + 21
             a1 =  46

So a1 = 46 is the first term of the sequence and d = -3 is the common
difference.   

So the arithmetic sequence is:

46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, -2, -5, -8, -11, -14, ...

The general term is found by substituting a1 = 46 and d = -3 in the
formula for the nth term:

an = a1 + (n - 1)d

an = 46 + (n - 1)(-3)

an = 46 - 3(n - 1)

an = 46 - 3n + 3

an = 49 - 3n

That's the general term.

Edwin