Question
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Answer
The sum of 5 from \( t = 6 \) to \( t = 40 \) is 175.
Solution
To evaluate the sum:
\[
\sum_{t=6}^{40} 5
\]
**Step 1: Understand the Summation**
This summation means you're adding the number **5** for each integer value of \( t \) starting from **6** up to **40**.
**Step 2: Determine the Number of Terms**
To find out how many times you're adding **5**, calculate the number of integers from **6** to **40** inclusive.
\[
\text{Number of terms} = (40 - 6) + 1 = 35
\]
**Step 3: Calculate the Sum**
Multiply the value being summed (**5**) by the number of terms (**35**):
\[
\sum_{t=6}^{40} 5 = 5 \times 35 = 175
\]
**Final Answer:**
\[
\sum_{t=6}^{40} 5 = 175
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To calculate the sum, we first note that \(5\) is a constant term being added for each integer from \(6\) to \(40\). The number of terms in this summation can be found by considering the endpoints of the summation: From \(6\) to \(40\), the number of terms \(n\) is given by: \[ n = 40 - 6 + 1 = 35 \] So, we are summing \(5\) a total of \(35\) times. This means the entire sum can be calculated as: \[ \sum_{t=6}^{40} 5 = 5 \times n = 5 \times 35 = 175 \] Thus, the final result for the sum \( \sum_{t=6}^{40} 5 \) is \(175\).
