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 5
- Pattern 42
- Pattern 211
(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 5
= 5 x 3 + 2
= 17
(b)
Number of dots for Pattern 42
= 42 x 3 + 2
= 128
(c)
Number of dots for Pattern 211
= 211 x 3 + 2
= 635
Answer(s): (a) 17; (b) 128; (c) 635