Shiyun used stars and sticks to make the following patterns.
- How many stars are there in Pattern 10?
- If Shiyun counted 441 stars, which pattern number had she made?
- How many stars are there in Pattern 85?
(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 10
= (10 + 1)
2
= 11
2= 11 x 11
= 121
(b)
(Pattern number + 1)
2 = 441
(Pattern number + 1) = √441 = 21
Pattern number = 21 - 1 = 20
(b)
Number of stars in Pattern 85
= (85 + 1)
2 = 86
2
= 86 x 86
= 7396
Answer(s): (a) 121; (b) 20; (c) 7396
