A child places n cubic building blocks in a row to form the base of a triangular design (see figure). Each successive row contains two fewer blocks than the preceding row. Find a formula for the number of blocks N used in the design. (Hint: The number of building blocks in the design depends on whether n is odd or even.)

Question

A child places n cubic building blocks in a row to form the base of a triangular design (see figure). Each successive row contains two fewer blocks than the preceding row. Find a formula for the number of blocks N used in the design. (Hint: The number of building blocks in the design depends on whether n is odd or even.)
If n is odd, N =	
 
If n is even, N =	
 
n is even in the block

Steve · Answer

Have you tried laying out a few rows? I'm sure you will see a pattern. You will be adding up sequences of even or odd numbers...