Use summation rules to find the following:
\[
\sum_{k=1}^{22}(3+5 k)=
\]

Step 1 ：The given sum is a sum of an arithmetic series. The general form of an arithmetic series is \(a + (a+d) + (a+2d) + ... + (a+nd)\), where \(a\) is the first term, \(d\) is the common difference, and \(n\) is the number of terms. In this case, \(a = 3\), \(d = 5\), and \(n = 22\).

Step 2 ：The sum of an arithmetic series can be found using the formula \(S = \frac{n}{2} * (a + l)\), where \(S\) is the sum, \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.

Step 3 ：The last term can be found using the formula \(l = a + (n-1)*d\). In this case, \(l = 3 + (22-1)*5 = 108\).

Step 4 ：Substituting the values into the sum formula, we get \(S = \frac{22}{2} * (3 + 108) = 1221.0\).

Step 5 ：The sum of the arithmetic series is 1221.0. This is the final answer.

Step 6 ：Final Answer: \(\boxed{1221.0}\)