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 9
- Pattern 23
- Pattern 258
(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 9
= 9 x 3 + 2
= 29
(b)
Number of dots for Pattern 23
= 23 x 3 + 2
= 71
(c)
Number of dots for Pattern 258
= 258 x 3 + 2
= 776
Answer(s): (a) 29; (b) 71; (c) 776