Step 1 :We are given an arithmetic series where the first term (a) is 9, the last term (l) is 123, and the common difference (d) is 6.
Step 2 :We can express this series using the summation notation. The formula for the sum of an arithmetic series is given by: \[S = \frac{n}{2}(a + l)\] where: S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
Step 3 :We can find the number of terms (n) using the formula: \[n = \frac{l - a}{d} + 1\] where d is the common difference.
Step 4 :Substituting the given values into the formula, we get: a = 9, l = 123, d = 6, n = 20.0
Step 5 :Substituting these values into the sum formula, we get: S = 1320.0
Step 6 :Final Answer: The sum of the arithmetic series $9+15+21+\ldots+123$ is \(\boxed{1320}\)