If 1 block equals 1 step, 3 blocks equals 2 steps, 6 blocks equals 3 steps, what is the total number of cubic blocks needed to build 6 steps?

If 1 block equals 1 step, 3 blocks equals 2 steps, 6 blocks equals 3 steps, what is the total number of cubic blocks needed to build 6 steps?

• A. 21
• B. 28
• C. 18
• D. 24

Answer: (A)

Each new step requires adding a row of blocks that matches the step’s number, so the total blocks after n steps is the sum 1 + 2 + 3 + ... + n. For 6 steps that becomes 1 + 2 + 3 + 4 + 5 + 6 = 21. This is a triangular-number pattern, and you can use the formula n(n+1)/2: 6 × 7 / 2 = 21. So 21 blocks are needed.

Each new step requires adding a row of blocks that matches the step’s number, so the total blocks after n steps is the sum 1 + 2 + 3 + ... + n. For 6 steps that becomes 1 + 2 + 3 + 4 + 5 + 6 = 21. This is a triangular-number pattern, and you can use the formula n(n+1)/2: 6 × 7 / 2 = 21. So 21 blocks are needed.