Question
\[ \sum_{a=3}^{9} 9 a \] How many terms are in the series?
Ask by King Simmons. 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:
\[
\sum_{a=3}^{9} 9a
\]
You can list out the values of \( a \) from 3 to 9:
\[
a = 3, 4, 5, 6, 7, 8, 9
\]
Counting these values:
\[
3, \ 4, \ 5, \ 6, \ 7, \ 8, \ 9 \quad \text{(7 terms)}
\]
**There are 7 terms in the series.**
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Simplify this solution Mind Expander
To find the number of terms in the series \( \sum_{a=3}^{9} 9 a \), we look at the range of \( a \) from 3 to 9, inclusive. The last term \( a=9 \) and the first term \( a=3 \). We can use the formula for the number of terms in an inclusive sequence, which is given by: \[ \text{Number of terms} = (\text{Last term} - \text{First term}) + 1 \] Plugging in the values: \[ \text{Number of terms} = (9 - 3) + 1 = 6 + 1 = 7 \] Thus, there are 7 terms in the series.
