Xandra used stars and sticks to make the following patterns.
- How many stars are there in Pattern 9?
- If Xandra counted 361 stars, which pattern number had she made?
- How many stars are there in Pattern 78?
(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 = 361
(Pattern number + 1) = √361 = 19
Pattern number = 19 - 1 = 18
(b)
Number of stars in Pattern 78
= (78 + 1)
2 = 79
2
= 79 x 79
= 6241
Answer(s): (a) 100; (b) 18; (c) 6241
