Emily used stars and sticks to make the following patterns.
- How many stars are there in Pattern 9?
- If Emily counted 169 stars, which pattern number had she made?
- How many stars are there in Pattern 82?
(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 = 169
(Pattern number + 1) = √169 = 13
Pattern number = 13 - 1 = 12
(b)
Number of stars in Pattern 82
= (82 + 1)
2 = 83
2
= 83 x 83
= 6889
Answer(s): (a) 100; (b) 12; (c) 6889
