Question: Determine \( S_5 \) \[ \sum_{k=1}^{n} 5k \]

Solution

Step 1: Identify the summation formula. \[ S_n = \sum_{k=1}^n 5k \] & Step 2: Substitute \( n = 5 \). \[ S_5 = \sum_{k=1}^5 5k \] & Step 3: Expand the summation. \[ S_5 = 5(1) + 5(2) + 5(3) + 5(4) + 5(5) \] & Step 4: Calculate each term. \[ S_5 = 5 + 10 + 15 + 20 + 25 \] & Step 5: Sum the terms. \[ S_5 = 75 \]