Emily used stars and sticks to make the following patterns.
- How many stars are there in Pattern 7?
- If Emily counted 225 stars, which pattern number had she made?
- How many stars are there in Pattern 62?
(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 = 225
(Pattern number + 1) = √225 = 15
Pattern number = 15 - 1 = 14
(b)
Number of stars in Pattern 62
= (62 + 1)
2 = 63
2
= 63 x 63
= 3969
Answer(s): (a) 64; (b) 14; (c) 3969
