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 78
- Pattern 414
(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 78
= 78 x 3 + 2
= 236
(c)
Number of dots for Pattern 414
= 414 x 3 + 2
= 1244
Answer(s): (a) 23; (b) 236; (c) 1244