\( \sum_{t=6}^{40} 5 \) Evaluate

To evaluate the sum: \[ \sum_{t=6}^{40} 5 \] This notation means that we are adding the number 5 for each integer value of \( t \) from 6 to 40, inclusive. Here's how to compute it step by step: 1. **Determine the Number of Terms:** The number of terms in the sum can be found by subtracting the lower limit from the upper limit and then adding 1 (since both endpoints are inclusive). \[ \text{Number of terms} = 40 - 6 + 1 = 35 \] 2. **Multiply by the Constant Value:** Since each term in the sum is 5, you multiply the number of terms by 5. \[ \text{Sum} = 35 \times 5 = 175 \] **Final Answer:** \[ \sum_{t=6}^{40} 5 = 175 \]