A pyramid is made of bricks. It is four bricks high with four bricks on the bottom row, 3 bricks on the row on top of that, then 2 bricks and then 1 brick. See Figure 1. How many total bricks would there be if the pyramid had 50 bricks on the base and it was 50 bricks high?

Solutions

• Find a pattern (formula) by Guess and Check.
• Use a spreadsheet.
• Add all the numbers with a calculator or pencil and paper.
• Use a geometric solution (the area of a triangle).
• Use the first and second differences to help find a pattern.
• Use a polynomial regression, along with info from the first and second differences, to find a formula on a spreadsheet or graphing calculator.
• Use matrices or a system of three equations and three unknowns to find the formula.
• Regroup the numbers and find a general pattern.