Penelope used stars and sticks to make the following patterns.
- How many stars are there in Pattern 7?
- If Penelope counted 256 stars, which pattern number had she made?
- How many stars are there in Pattern 107?
(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 7
= (7 + 1)
2
= 8
2= 8 x 8
= 64
(b)
(Pattern number + 1)
2 = 256
(Pattern number + 1) = √256 = 16
Pattern number = 16 - 1 = 15
(b)
Number of stars in Pattern 107
= (107 + 1)
2 = 108
2
= 108 x 108
= 11664
Answer(s): (a) 64; (b) 15; (c) 11664
