Jake arranged 3 beads and 3 sticks to form Pattern 1. Then he added 3 more beads and 6 sticks to form Pattern 2. He continued to form patterns in the same way.
- How many beads will he need to form Pattern 5?
- How many sticks will he need to form Pattern 7?
(a)
Pattern for the number of beads
Pattern 1: 1 + 2 = 3
Pattern 2: 1 + 2 + 3 = 6
Pattern 3: 1 + 2 + 3 + 4 = 10
Formula:
Number of beads
= 1 + 2 + 3 + ... + (Pattern Number + 1)
=
(Pattern Number +1) x (Pattern Number + 2)2 Number of beads for Pattern 5
= 1 + 2 + 3 + ... + (5 + 1)
= 1 + 2 + 3 + ... + 6
=
6 x 72= 21
(b)
Pattern for the number of sticks
Pattern 1: 3 x (1) = 3
Pattern 2: 3 x (1 + 2) = 9
Pattern 3: 3 x (1 + 2 + 3) = 18
Formula:
Number of sticks
= 3 x (1 + 2 + 3 + ... + Pattern number)
= 3 x
Pattern Number x (Pattern Number + 1)2Number of sticks for Pattern 7
= 3 x (1 + 2 + 3 + ... + 7)
= 3 x (
7 x 82)
= 84
Answer(s): (a) 21; (b) 84