The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 9 have?
- How many blocks will Pattern 42 have?
- Which pattern has 421 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 42
= 42 x (42 - 1) + 1
= 42 x 41 + 1
= 1723
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 421
Pattern number x (Pattern number - 1) = 421 - 1 = 420
21 x 20 = 420
Pattern number = 21
Answer(s): (a) 73; (b) 1723; (c) 21