In a pattern, rectangles are divided into sections: Stage 1 has 2 sections, Stage 2 has 4 sections, Stage 3 has 8 sections, Stage 4 has 16 sections. Which formula represents the number of sections at Stage n?
A2n
B2^n
Cn²
Dn + 2
Correct Answer:
B. 2^n
EXPLANATION
The sequence follows powers of 2: 2¹=2, 2²=4, 2³=8, 2⁴=16. At stage n, there are 2^n sections, making this exponential growth.
A sequence shows triangles with increasing internal lines: First triangle has 0 internal lines, second has 1 diagonal line, third has 2 intersecting diagonals, fourth has 3 lines forming internal divisions. How many internal lines will the fifth triangle have?
A4 lines
B5 lines
C6 lines
D7 lines
Correct Answer:
A. 4 lines
EXPLANATION
The pattern shows arithmetic progression: 0, 1, 2, 3, therefore the next number is 4. Each triangle gains one additional internal line.
In a pattern, small circles arrange around a central square. Pattern 1 has 4 circles, Pattern 2 has 8 circles, Pattern 3 has 12 circles. How many circles in Pattern 5?
A20 circles
B24 circles
C16 circles
D28 circles
Correct Answer:
A. 20 circles
EXPLANATION
The pattern increases by 4 each time: 4, 8, 12, 16, 20. This is arithmetic progression with common difference 4.
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