This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The question is asking for the rule for the total number of blocks in each building. Step 1: Calculate the total number of blocks for the first few buildings. Building 1: 1 block (Level 1: 1) Building 2: 2 + 1 = 3 blocks (Level 1: 2, Level 2: 1) Building 3: 3 + 2 + 1 = 6 blocks (Level 1: 3, Level 2: 2, Level 3: 1) Building 4: 4 + 3 + 2 + 1 = 10 blocks (Level 1: 4, Level 2: 3, Level 3: 2, Level 4: 1) Step 2: Identify the pattern. The sequence of total blocks is 1, 3, 6, 10. This is the sequence of triangular numbers. Step 3: State the rule. The rule for the total number of blocks in Building n is the sum of integers from 1 to n. This can be expressed by the formula: Total blocks = (n(n+1))/(2) Where n is the building number. For example: For Building 1 (n=1): (1(1+1))/(2) = (1 × 2)/(2) = 1 For Building 2 (n=2): (2(2+1))/(2) = (2 × 3)/(2) = 3 For Building 3 (n=3): (3(3+1))/(2) = (3 × 4)/(2) = 6 For Building 4 (n=4): (4(4+1))/(2) = (4 × 5)/(2) = 10 The rule for the total number of blocks in Building n is (n(n+1))/(2). 3 done, 2 left today. You're making progress.