The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 6 have?
- How many blocks will Pattern 35 have?
- Which pattern has 133 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 6
= 6 x (6 - 1) + 1
= 6 x 5 + 1
= 31
(b)
Number of blocks for Pattern 35
= 35 x (35 - 1) + 1
= 35 x 34 + 1
= 1191
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 133
Pattern number x (Pattern number - 1) = 133 - 1 = 132
12 x 11 = 132
Pattern number = 12
Answer(s): (a) 31; (b) 1191; (c) 12