Answer:
The nth term of the arithmetic sequence is given by:
.....[1]
and
the sum of the arithmetic sequence is:
.....[2]
where,
a is the first term
d is the common difference of two consecutive term
l is the last term in the series
As per the statement:
The finite arithmetic series 4+8+12+16...+76
here, a = 4 and
Common difference(d) = 4
Since,
8-4 = 4,
12-8 = 4,
16-12 = 4 and so on
last term of the finite series(l) = 76
Substitute these in [1] we have

Using distributive property, 

Simplify:

Divide both sides by 4 we have;
19 = n
or
n= 19
Substitute the given value and n = 19 in [2]

Therefore, the sum of the given finite arithmetic series is, 760