The sequence of patterns is formed with squares. The first three patterns are shown.
- How many squares are needed in pattern 31?
- Which pattern number contains 445 squares?
(a)
Pattern for the total number of squares
Pattern 1: 7 squares = 1 x 3 + 4
Pattern 2: 10 squares = 2 x 3 + 4
Pattern 3: 13 squares = 3 x 3 + 4
Formula:
Total number of squares = Pattern number x 3 + 4
Number of squares in Pattern 31
= 31 x 3 + 4
= 97
(b)
Pattern number x 3 + 4 = 445
Pattern number x 3 = 445 - 4
Pattern number x 3 = 441
Pattern number
= 441 ÷ 3
= 147
Answer(s); (a) 97; (b) 147
