The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 10 have?
- How many blocks will Pattern 18 have?
- Which pattern has 31 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 18
= 18 x (18 - 1) + 1
= 18 x 17 + 1
= 307
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 31
Pattern number x (Pattern number - 1) = 31 - 1 = 30
6 x 5 = 30
Pattern number = 6
Answer(s): (a) 91; (b) 307; (c) 6
