Remark: L = a + (n - 1)d is your starting point. In order to find the sum, you must know the value of n.
Givens: a = - 8; d=5; L = 67
Substitute and solve
67 = - 8 + (n - 1)*5 Add 8 to both sides.
67 + 8 = -8 + 8 + (n - 1)*5
75 = (n - 1)*5 Divide by 5 on both sides.
15 = n - 1 Add one to get the answer.
16 = n
Part Two: Use The summation notation to find the sum. Unfortunately, I don't know how to do this in latex.
Sum (n = 1 to 16) -8 + 5*(n - 1)