Julie used stars and sticks to make the following patterns.
- How many stars are there in Pattern 7?
- If Julie counted 400 stars, which pattern number had she made?
- How many stars are there in Pattern 114?
(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 = 400
(Pattern number + 1) = √400 = 20
Pattern number = 20 - 1 = 19
(b)
Number of stars in Pattern 114
= (114 + 1)
2 = 115
2
= 115 x 115
= 13225
Answer(s): (a) 64; (b) 19; (c) 13225
