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 6
- Pattern 54
- Pattern 241
(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 6
= 6 x 3 + 2
= 20
(b)
Number of dots for Pattern 54
= 54 x 3 + 2
= 164
(c)
Number of dots for Pattern 241
= 241 x 3 + 2
= 725
Answer(s): (a) 20; (b) 164; (c) 725