Fanny used stars and sticks to make the following patterns.
- How many stars are there in Pattern 7?
- If Fanny counted 324 stars, which pattern number had she made?
- How many stars are there in Pattern 49?
(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 7
= (7 + 1)
2
= 8
2= 8 x 8
= 64
(b)
(Pattern number + 1)
2 = 324
(Pattern number + 1) = √324 = 18
Pattern number = 18 - 1 = 17
(b)
Number of stars in Pattern 49
= (49 + 1)
2 = 50
2
= 50 x 50
= 2500
Answer(s): (a) 64; (b) 17; (c) 2500
