The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 8 have?
- How many blocks will Pattern 16 have?
- Which pattern has 43 blocks?
(a)
Pattern for the number of blocks
Pattern 1: 1 x 0 + 1 = 1
Pattern 2: 2 x 1 + 1 = 3
Pattern 3: 3 x 2 + 1 = 7
Number of blocks = Pattern number x (Pattern number - 1) + 1
Number of blocks for Pattern 8
= 8 x (8 - 1) + 1
= 8 x 7 + 1
= 57
(b)
Number of blocks for Pattern 16
= 16 x (16 - 1) + 1
= 16 x 15 + 1
= 241
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 43
Pattern number x (Pattern number - 1) = 43 - 1 = 42
7 x 6 = 42
Pattern number = 7
Answer(s): (a) 57; (b) 241; (c) 7