Find the sum. \( \sum_{i=1}^{26}(4 i+7) \) The sum is \( \square \)

To find the sum \( \sum_{i=1}^{26}(4i+7) \), we can break it down into two separate sums: \[ \sum_{i=1}^{26}(4i + 7) = \sum_{i=1}^{26}4i + \sum_{i=1}^{26}7 \] For the first sum, \( \sum_{i=1}^{26}4i \): \[ \sum_{i=1}^{26}4i = 4 \sum_{i=1}^{26}i = 4 \cdot \frac{26(26 + 1)}{2} = 4 \cdot \frac{26 \cdot 27}{2} = 4 \cdot 351 = 1404 \] For the second sum, \( \sum_{i=1}^{26}7 \): \[ \sum_{i=1}^{26}7 = 7 \cdot 26 = 182 \] Now, we can combine the results: \[ \sum_{i=1}^{26}(4i + 7) = 1404 + 182 = 1586 \] Thus, the sum is \( \boxed{1586} \).