Question
\[ \sum_{a=3}^{9} 9 a \] How many terms are in the series?
Ask by Boone Fowler. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are 7 terms in the series.
Solution
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 \(\sum_{a=3}^{9} 9a\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
When evaluating the sum \( \sum_{a=3}^{9} 9a \), we need to determine the number of terms in the series. The series starts at \( a=3 \) and ends at \( a=9 \). To find the number of terms, we can use the formula for the number of terms in a series ranging from \( a \) to \( b \): \[ \text{Number of terms} = b - a + 1 \] Substituting \( a = 3 \) and \( b = 9 \): \[ \text{Number of terms} = 9 - 3 + 1 = 7 \] Thus, there are 7 terms in the series.
