The sequence of patterns is formed with squares. The first three patterns are shown.
- How many squares are needed in pattern 27?
- Which pattern number contains 499 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 27
= 27 x 3 + 4
= 85
(b)
Pattern number x 3 + 4 = 499
Pattern number x 3 = 499 - 4
Pattern number x 3 = 495
Pattern number
= 495 ÷ 3
= 165
Answer(s); (a) 85; (b) 165
