The diagram shows a sequence of patterns formed by square tiles. By considering the pattern information in the table, answer the questions.
- Find the number of tiles at the bottom layer in the 50th pattern
- Find the total number of tiles in Pattern 39.
(a)
Pattern for the number of tiles in the bottom layer
Pattern 1: 1 x 2 - 1 = 1
Pattern 2: 2 x 2 - 1 = 3
Pattern 3: 3 x 2 - 1 = 5
Number of tiles in the bottom layer = Pattern number x 2 - 1
Number of tiles in the bottom layer of Pattern 50
= 50 x 2 - 1
= 99
(b)
Pattern for the total number of tiles
Pattern 1: 1 = 1
Pattern 2: 1 + 3 = 4
Pattern 3: 1 + 3 + 5 = 9
Total number of tiles = Pattern number
2 Total number of tiles for Pattern 39
= 39
2 = 1521
Answer(s): (a) 99; (b) 1521
