The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 8 have?
- How many blocks will Pattern 38 have?
- Which pattern has 91 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 38
= 38 x (38 - 1) + 1
= 38 x 37 + 1
= 1407
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 91
Pattern number x (Pattern number - 1) = 91 - 1 = 90
10 x 9 = 90
Pattern number = 10
Answer(s): (a) 57; (b) 1407; (c) 10