Using dots to form a series of inverted T-shaped patterns, the first three patterns are as shown. Find the number of dots needed to form the following patterns.
- Pattern 4
- Pattern 31
- Pattern 107
(a)
Pattern for the number of dots
Pattern 1: 1 x 3 + 2 = 5
Pattern 2: 2 x 3 + 2 = 8
Pattern 3: 3 x 3 + 2 = 11
Formula
Number of dots = Pattern number x 3 + 2
Number of dots for Pattern 4
= 4 x 3 + 2
= 14
(b)
Number of dots for Pattern 31
= 31 x 3 + 2
= 95
(c)
Number of dots for Pattern 107
= 107 x 3 + 2
= 323
Answer(s): (a) 14; (b) 95; (c) 323