Olivia used stars and sticks to make the following patterns.
- How many stars are there in Pattern 9?
- If Olivia counted 256 stars, which pattern number had she made?
- How many stars are there in Pattern 93?
(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 9
= (9 + 1)
2
= 10
2= 10 x 10
= 100
(b)
(Pattern number + 1)
2 = 256
(Pattern number + 1) = √256 = 16
Pattern number = 16 - 1 = 15
(b)
Number of stars in Pattern 93
= (93 + 1)
2 = 94
2
= 94 x 94
= 8836
Answer(s): (a) 100; (b) 15; (c) 8836