Two ways to find it, the "thinking" way, and the "robotic" way:

Method 1.  By writing the series in reverse order and adding, a method
           in which you understand why it works.

Method 2.  By using two memorized formulas that you have no idea
           why they work.

Method 1:

8 + 9 + 10 + 11 + ... 397 + 398 + 399 + 400

 8 is term #1, and 1 is 7 less than  8
 9 is term #2, and 2 is 7 less than  9
10 is term #3, and 3 is 7 less than 10
11 is term #4, and 4 is 7 less than 11

Therefore we conclude that 400 is term #393 
because 393 is 7 less than 400.

So there are 393 terms.

Write the sequence and underneath write the sequence in
reverse order:

  Sum =   8 +   9 +  10 +  11 + ... + 397 + 398 + 399 + 400
  Sum = 400 + 399 + 398 + 397 + ... +  11 +  10 +   9 +   8

Now draw a line underneath and add them term by term:

  Sum =   8 +   9 +  10 +  11 + ... + 397 + 398 + 399 + 400
  Sum = 400 + 399 + 398 + 397 + ... +  11 +  10 +   9 +   8
---------------------------------------------------
2×Sum = 408 + 408 + 408 + 408 + ... + 408 + 408 + 408 + 408

So we have 393 terms each of which is 408.

2×Sum = 393×408 = 160344

Therefore the sum is half of that

  Sum = ×156264 = 80172

=======================================================

Method 2:

Memorize these two formula which you have no idea why they works.

an = a1 + (n-1)d

Sn = (a1 + an)

where a1 = first term = 8
n = the number of terms
d = the difference between any term and the one before it = 1 
an = the nth term
Sn = the sum of the first n terms.

We use the first memorized formula to find n:

an = a1 + (n-1)d
400 = 8 + (n-1)(1)
400 = 8 + n - 1
400 = 7 + n
393 = n

Then we substitute in the sum formula we have memorized:

Sn = (a1 + an)
S393 = (8 + 400)
S393 = (408)
S393 = 80172 

Edwin