In a composite pattern, concentric circles alternate with squares: Circle (1 region), Square-Circle (4 regions), Square-Circle-Square (9 regions), Square-Circle-Square-Circle (16 regions). How many regions will the next figure have?
A20 regions
B24 regions
C25 regions
D30 regions
Correct Answer:
C. 25 regions
EXPLANATION
The pattern shows perfect squares: 1², 2², 3², 4², so the next is 5² = 25 regions. Each figure follows the pattern of adding alternating shapes creating n² distinct regions.
A pattern shows pentagons with vertices colored: Stage 1 has 1 vertex colored, Stage 2 has 3 vertices colored, Stage 3 has 6 vertices colored, Stage 4 has 10 vertices colored. What is the pattern rule?
ATriangular numbers (n(n+1)/2)
BSquare numbers (n²)
CFibonacci sequence
DPrime numbers
Correct Answer:
A. Triangular numbers (n(n+1)/2)
EXPLANATION
The sequence 1, 3, 6, 10 represents triangular numbers: 1(2)/2=1, 2(3)/2=3, 3(4)/2=6, 4(5)/2=10. Each stage n has n(n+1)/2 colored vertices.