Question 1062612
<pre>
I have a problem with your typo "trice".  There is such
a word in the dictionary.  However "trice" means "in a 
moment" or "very quickly."  You could have meant "twice",
which means "two times", or you could have meant "thrice"
which means "three times".  I will assume you meant "twice".

Here are the first 8 terms:

a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d, a+7d
</pre>
The third term of an A.P. is 4 more than twice the first term.
<pre>
 a+2d = 2a+4
   2d = a+4
 2d-4 = a
</pre>
The 8th term is 4 less than "trice" the third term.
<pre>
Assuming "trice" means "twice",

 a+7d = 2(a+2d)-4
 a+7d = 2a+4d-4
   3d = a-4
 3d+4 = a
 3d+4 = a
 
and since 2d-4 = a,
          2d-4 = 3d+4 
            -8 = d

          2d-4 = a
       2(-8)-4 = a
         -16-4 = a
           -20 = a    


Fifth term = a+4d = -20+4(-8) = -20-32 = -52.

That's the answer.

Checking:

The A.P. is

a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d, a+7d

-20, -20+(-8), -20+2(-8), -20+3(-8), -20+4(-8), -20+5(-8), -20+6(-8), -20+7(-8)  

-20, -20-8, -20-16, -20-24, -20-32, -20-40, -20-48, -20-56

-20, -28, -36, -33, -52, -60, -68, -76

Checking the first sentence:

The third term of an A.P. is 4 more than twice the first term.

-36 is 4 more than twice -20.
Twice -20 is -40, and 4 more is -40+4 = -36.  That checks.

Checking the second sentence:

The 8th term is 4 less than twice the third term

-76 is 4 less than twice -36

Twice -36 is -72, and 4 less than that is -72-4 = -76.
That checks too, so if "trice" means "twice", then this
is correct.

Edwin</pre>