The diagram shows the number of blocks in the pattern.
- How many blocks will Pattern 6 have?
- How many blocks will Pattern 50 have?
- Which pattern has 31 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 50
= 50 x (50 - 1) + 1
= 50 x 49 + 1
= 2451
(c)
Using guess and check.
Pattern number x (Pattern number - 1) + 1 = 31
Pattern number x (Pattern number - 1) = 31 - 1 = 30
6 x 5 = 30
Pattern number = 6
Answer(s): (a) 31; (b) 2451; (c) 6