Cathy used stars and sticks to make the following patterns.
- How many stars are there in Pattern 8?
- If Cathy counted 625 stars, which pattern number had she made?
- How many stars are there in Pattern 42?
(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 = 625
(Pattern number + 1) = √625 = 25
Pattern number = 25 - 1 = 24
(b)
Number of stars in Pattern 42
= (42 + 1)
2 = 43
2
= 43 x 43
= 1849
Answer(s): (a) 81; (b) 24; (c) 1849
