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 8
- Pattern 55
- Pattern 418
(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 8
= 8 x 3 + 2
= 26
(b)
Number of dots for Pattern 55
= 55 x 3 + 2
= 167
(c)
Number of dots for Pattern 418
= 418 x 3 + 2
= 1256
Answer(s): (a) 26; (b) 167; (c) 1256