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 7
- Pattern 86
- Pattern 228
(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 7
= 7 x 3 + 2
= 23
(b)
Number of dots for Pattern 86
= 86 x 3 + 2
= 260
(c)
Number of dots for Pattern 228
= 228 x 3 + 2
= 686
Answer(s): (a) 23; (b) 260; (c) 686