To find the sum of an arithmetic series, we can use the formula:

Sn = (n/2)(a + l)

where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

In this case, the first term (a) is 1, the last term (l) is 178, and the common difference (d) is 3 (since each term increases by 3).

To find the number of terms (n), we can use the formula:

l = a + (n-1)d

Substituting the given values:

178 = 1 + (n-1)(3)
178 = 1 + 3n - 3
178 + 2 = 3n
180 = 3n
n = 60

Now we can substitute the values into the sum formula:

Sn = (n/2)(a + l)
Sn = (60/2)(1 + 178)
Sn = 30(179)
Sn = 5,370

Therefore, the sum of the series 1 + 4 + 7 + 10 + ... + 178 is 5,370.