Problem
Each layer adds 2 more, so extending to 7 layers gives 1,3,5,7,9,11,13 blocks.
Each L-shaped layer is built by adding one block to the top of the rising side and one to the end of the bottom row, so it always has exactly 2 more than the layer before. That same step repeats for every layer, so after 1, 3, 5, 7 the counts keep climbing by 2 to 9, 11, 13.
Look For A Pattern4.OA.C.5Finding PatternsThe seven layers use 1, 3, 5, 7, 9, 11, 13 blocks, and each layer holds 2 more blocks than the one before it.
Each L-shaped layer is built from the previous one by setting one extra block on top of its rising side and one extra block on the end of its bottom row.
The taller side and the longer bottom row are separate parts of the figure that share no block, so the new figure's count is the old count plus those two added blocks.
Because that same building step repeats for every layer, each count is the one before it plus 2, so after 1, 3, 5, 7 the counts keep climbing to 9, 11, 13.
Reaching each next layer's count means adding the same fixed amount, 2, onto the running count over and over.
Adding layers 1 through 7 gives 1+3+5+7+9+11+13=49 blocks in all.
The total block count is exactly the seven separate layer counts added together with nothing shared between them. Adding 1, 3, 5, 7, 9, 11, 13 one by one collects every layer's blocks into the full total.
Solve An Easier Related Problem4.OA.A.3Finding PatternsExtend the +2 rule all the way out, then add every layer together to get the total block count.