Use the formula \( S=n^{2} \) to find the sum of \( 1+3+5+\cdots+551 \). (Hint: To find \( n \), add 1 to the last term and divide by 2.) \( 1+3+5+\cdots+551=\square \) (Simplify your answer.)

To find the sum \( 1 + 3 + 5 + \cdots + 551 \) using the formula \( S = n^2 \), follow these steps: 1. **Determine the number of terms (\( n \)):** The last term of the sequence is 551. According to the hint: \[ n = \frac{\text{last term} + 1}{2} = \frac{551 + 1}{2} = \frac{552}{2} = 276 \] 2. **Calculate the sum using the formula \( S = n^2 \):** \[ S = 276^2 = 76176 \] So, the sum of the series is: \[ 1 + 3 + 5 + \cdots + 551 = 76176 \] **Answer:** \( 1+3+5+\cdots+551=76176 \)