The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 7 have?
- How many blocks will Pattern 37 have?
- Which pattern has 343 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 37
= 37 x (37 - 1) + 1
= 37 x 36 + 1
= 1333
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 343
Pattern number x (Pattern number - 1) = 343 - 1 = 342
19 x 18 = 342
Pattern number = 19
Answer(s): (a) 43; (b) 1333; (c) 19