Hilda used stars and sticks to make the following patterns.
- How many stars are there in Pattern 8?
- If Hilda counted 400 stars, which pattern number had she made?
- How many stars are there in Pattern 116?
(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 = 400
(Pattern number + 1) = √400 = 20
Pattern number = 20 - 1 = 19
(b)
Number of stars in Pattern 116
= (116 + 1)
2 = 117
2
= 117 x 117
= 13689
Answer(s): (a) 81; (b) 19; (c) 13689
