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
The third term of an A.P. is 4 more than twice the first term.
a+2d = 2a+4
2d = a+4
2d-4 = a
The 8th term is 4 less than "trice" the third term.
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
