The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 9 have?
- How many blocks will Pattern 20 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 9
= 9 x (9 - 1) + 1
= 9 x 8 + 1
= 73
(b)
Number of blocks for Pattern 20
= 20 x (20 - 1) + 1
= 20 x 19 + 1
= 381
(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) 73; (b) 381; (c) 13