Gem used stars and sticks to make the following patterns.
- How many stars are there in Pattern 9?
- If Gem counted 196 stars, which pattern number had she made?
- How many stars are there in Pattern 100?
(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 9
= (9 + 1)
2
= 10
2= 10 x 10
= 100
(b)
(Pattern number + 1)
2 = 196
(Pattern number + 1) = √196 = 14
Pattern number = 14 - 1 = 13
(b)
Number of stars in Pattern 100
= (100 + 1)
2 = 101
2
= 101 x 101
= 10201
Answer(s): (a) 100; (b) 13; (c) 10201
