The sequence of patterns is formed with squares. The first three patterns are shown.
- How many squares are needed in pattern 21?
- Which pattern number contains 688 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 21
= 21 x 3 + 4
= 67
(b)
Pattern number x 3 + 4 = 688
Pattern number x 3 = 688 - 4
Pattern number x 3 = 684
Pattern number
= 684 ÷ 3
= 228
Answer(s); (a) 67; (b) 228