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
You're on a roll — here are the answers for all the questions: 1. Draw the next building in the sequence. The next building (Building 4) will have 4 blocks in the bottom layer, 3 blocks in the next layer, 2 blocks in the layer above that, and 1 block at the very top. c \\ \\ \\ 2. Count the blocks in level 1 of each building. In the table below, fill in the number of blocks in level 1 for buildings 1, 2, 3 and 4. 5. Use the rule to fill in the number of blocks in level 1 for buildings with 6 levels, 10 levels, 12 levels and 20 levels. Enter this in the table. The number of blocks in Level 1 for Building n (which has n levels) is n. The completed table for questions 2 and 5 is: |c|c|c|c|c|c|c|c| Building number & 1 & 2 & 3 & 4 & 6 & 10 & 12 \\ Blocks in level 1 & 1 & 2 & 3 & 4 & 6 & 10 & 12 \\ For a building with 20 levels, the number of blocks in Level 1 is 20. 3. Write down the rule for the pattern of numbers. This refers to the total number of blocks in each building. The rule for the total number of blocks in Building n is the sum of integers from 1 to n. Total blocks = (n(n+1))/(2) 4. Test your rule for buildings 3 and 4 using number sentence. The rule for total blocks is (n(n+1))/(2). For Building 3 (n=3): Number sentence: 1+2+3 = 6 Using the rule: (3(3+1))/(2) = (3 × 4)/(2) = (12)/(2) = 6. The rule holds. For Building 4 (n=4): Number sentence: 1+2+3+4 = 10 Using the rule: (4(4+1))/(2) = (4 × 5)/(2) = (20)/(2) = 10. The rule holds. 6. Calculate the number of levels that a building will have if it has 3; 9; 21; 60; 63 blocks in level 1. Enter this in the table. If a building has X blocks in Level 1, then the building number (and thus the number of levels) is X. If Level 1 has 3 blocks: Number of levels = 3. If Level 1 has 9 blocks: Number of levels = 9. If Level 1 has 21 blocks: Number of levels = 21. If Level 1 has 60 blocks: Number of levels = 60. If Level 1 has 63 blocks: Number of levels = 63. What's next?