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 53
- Pattern 463
(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 53
= 53 x 3 + 2
= 161
(c)
Number of dots for Pattern 463
= 463 x 3 + 2
= 1391
Answer(s): (a) 29; (b) 161; (c) 1391