The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 10 have?
- How many blocks will Pattern 16 have?
- Which pattern has 57 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 10
= 10 x (10 - 1) + 1
= 10 x 9 + 1
= 91
(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 = 57
Pattern number x (Pattern number - 1) = 57 - 1 = 56
8 x 7 = 56
Pattern number = 8
Answer(s): (a) 91; (b) 241; (c) 8
