Vanessa used stars and sticks to make the following patterns.
- How many stars are there in Pattern 6?
- If Vanessa counted 196 stars, which pattern number had she made?
- How many stars are there in Pattern 72?
(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 6
= (6 + 1)
2
= 7
2= 7 x 7
= 49
(b)
(Pattern number + 1)
2 = 196
(Pattern number + 1) = √196 = 14
Pattern number = 14 - 1 = 13
(b)
Number of stars in Pattern 72
= (72 + 1)
2 = 73
2
= 73 x 73
= 5329
Answer(s): (a) 49; (b) 13; (c) 5329