One rule, written once, for every step

A plus shape of tiles grows each step: 5, 9, 13, 17. How many tiles does step 40 need?

Step 40 needs 161 tiles. No earlier step is built. Here n is the step number.

Rule: four arms of n, plus the middle tile, is 4n + 1. Four arms of n tiles make 4n tiles. The middle tile adds 1. Check it: at n = 1, 4×1+1 = 5. At n = 4, 4×4+1 = 17.

Step 40: 4 × 40 + 1 = 161 tiles.

Which step has 101 tiles? Take away the middle tile: 101 − 1 = 100. The four arms share 100 tiles. 100 ÷ 4 = 25, so each arm has 25 tiles. That is step 25.

Slide the step to see the tiles. Then answer the question with 4n + 1.

Try the lab to finish this lesson.