Problem

Express the arithmetic sum using summation nota
\[
9+15+21+\ldots+123
\]

Answer

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Answer

Final Answer: The sum of the arithmetic series $9+15+21+\ldots+123$ is \(\boxed{1320}\)

Steps

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 \(\boxed{1320}\)

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