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 100, 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:

100 = 1 + (n-1)3
100 = 1 + 3n - 3
100 = 3n - 2
3n = 102
n = 34

Now we can substitute the values into the sum formula:

Sn = n/2 * (a + l)
Sn = 34/2 * (1 + 100)
Sn = 17 * 101
Sn = 1717

Therefore, the sum of the series 1 + 4 + 7 + .... + 97 + 100 is 1717.