Vanessa used stars and sticks to make the following patterns.
- How many stars are there in Pattern 8?
- If Vanessa counted 484 stars, which pattern number had she made?
- How many stars are there in Pattern 54?
(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 8
= (8 + 1)
2
= 9
2= 9 x 9
= 81
(b)
(Pattern number + 1)
2 = 484
(Pattern number + 1) = √484 = 22
Pattern number = 22 - 1 = 21
(b)
Number of stars in Pattern 54
= (54 + 1)
2 = 55
2
= 55 x 55
= 3025
Answer(s): (a) 81; (b) 21; (c) 3025
