The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 7 have?
- How many blocks will Pattern 31 have?
- Which pattern has 157 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 7
= 7 x (7 - 1) + 1
= 7 x 6 + 1
= 43
(b)
Number of blocks for Pattern 31
= 31 x (31 - 1) + 1
= 31 x 30 + 1
= 931
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 157
Pattern number x (Pattern number - 1) = 157 - 1 = 156
13 x 12 = 156
Pattern number = 13
Answer(s): (a) 43; (b) 931; (c) 13