Olivia used stars and sticks to make the following patterns.
- How many stars are there in Pattern 6?
- If Olivia counted 144 stars, which pattern number had she made?
- How many stars are there in Pattern 46?
(a)
Number of stars
Pattern 1: 4 = (1 + 1)
2
Pattern 2: 9 = (2 + 1)
2Pattern 3: 16 = (3 + 1)
2Formula:
Number of stars = (Pattern number + 1)
2 Number of stars in Pattern 6
= (6 + 1)
2
= 7
2= 7 x 7
= 49
(b)
(Pattern number + 1)
2 = 144
(Pattern number + 1) = √144 = 12
Pattern number = 12 - 1 = 11
(b)
Number of stars in Pattern 46
= (46 + 1)
2 = 47
2
= 47 x 47
= 2209
Answer(s): (a) 49; (b) 11; (c) 2209
