Marion used stars and sticks to make the following patterns.
- How many stars are there in Pattern 5?
- If Marion counted 324 stars, which pattern number had she made?
- How many stars are there in Pattern 61?
(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 5
= (5 + 1)
2
= 6
2= 6 x 6
= 36
(b)
(Pattern number + 1)
2 = 324
(Pattern number + 1) = √324 = 18
Pattern number = 18 - 1 = 17
(b)
Number of stars in Pattern 61
= (61 + 1)
2 = 62
2
= 62 x 62
= 3844
Answer(s): (a) 36; (b) 17; (c) 3844
