\[ \sum_{a=3}^{9} 9 a \] How many terms are in the series?

To determine the number of terms in the series \(\sum_{a=3}^{9} 9a\), we need to identify all the integer values that \(a\) takes from the starting point to the endpoint, including both. 1. **Identify the range of \(a\):** - **Starting value:** \(a = 3\) - **Ending value:** \(a = 9\) 2. **List the integer values of \(a\) within this range:** \[ a = 3, \ 4, \ 5, \ 6, \ 7, \ 8, \ 9 \] 3. **Count the number of terms:** - The terms correspond to each value of \(a\) listed. - Counting them: \(3\), \(4\), \(5\), \(6\), \(7\), \(8\), \(9\) — which amounts to **7 terms**. **Conclusion:** There are **7 terms** in the series \(\sum_{a=3}^{9} 9a\).