Gwen used stars and sticks to make the following patterns.
- How many stars are there in Pattern 10?
- If Gwen counted 484 stars, which pattern number had she made?
- How many stars are there in Pattern 89?
(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 10
= (10 + 1)
2
= 11
2= 11 x 11
= 121
(b)
(Pattern number + 1)
2 = 484
(Pattern number + 1) = √484 = 22
Pattern number = 22 - 1 = 21
(b)
Number of stars in Pattern 89
= (89 + 1)
2 = 90
2
= 90 x 90
= 8100
Answer(s): (a) 121; (b) 21; (c) 8100
