To find the number of terms in the given series, we need to determine the pattern and calculate the number of terms between the first term (117) and the last term (333).

Looking at the series, we can observe that each term is obtained by adding 3 to the previous term. So, we have a common difference of 3 between consecutive terms.

To find the number of terms, we can calculate the common difference between the first term and the last term:

333 - 117 = 216

To get the number of terms, we need to divide this difference by the common difference (3) and add 1:

Number of terms = (333 - 117) / 3 + 1 = 216 / 3 + 1 = 72 + 1 = 73

Therefore, the correct answer is Option 2: 73.

To further verify this, we can check the sum of the series using the formula for the sum of an arithmetic series:

Sum = (n/2) * (first term + last term)

Plugging in the values:

Sum = (73/2) * (117 + 333) = 36.5 * 450 = 16,425

Now let`s calculate the sum of the series by actually adding up the terms:

117 + 120 + 123 + ... + 333 = 16,425

Both methods yield the same sum, confirming that the number of terms is indeed 73.