Question 1
Identify the scaling rule in this sequence:
Figure 1:
Figure 2:
Figure 3:
Figure 4:
Select the next figure:
PATTERN ANALYSIS:
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 15 units
- Figure 2: radius = 20 units
- Figure 3: radius = 25 units
- Figure 4: radius = 30 units
Step 2: Calculate size changes between consecutive figures
- Fig 1 โ 2: 20 - 15 = 5 units
- Fig 2 โ 3: 25 - 20 = 5 units
- Fig 3 โ 4: 30 - 25 = 5 units
RULE HYPOTHESIS:
The circle radius increases by 5 units (linear progression)
VERIFICATION:
All consecutive differences are consistent: 5 units โ
APPLICATION:
Figure 5 radius = 30 + 5 = 35 units
SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = 5
COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type
Step 1: Measure the radius of circles in each figure
- Figure 1: radius = 15 units
- Figure 2: radius = 20 units
- Figure 3: radius = 25 units
- Figure 4: radius = 30 units
Step 2: Calculate size changes between consecutive figures
- Fig 1 โ 2: 20 - 15 = 5 units
- Fig 2 โ 3: 25 - 20 = 5 units
- Fig 3 โ 4: 30 - 25 = 5 units
RULE HYPOTHESIS:
The circle radius increases by 5 units (linear progression)
VERIFICATION:
All consecutive differences are consistent: 5 units โ
APPLICATION:
Figure 5 radius = 30 + 5 = 35 units
SCALING PATTERN TYPES:
- Linear arithmetic progression: constant d = 5
COMMON MISTAKES TO AVOID:
- Confusing diameter with radius
- Assuming linear when pattern is geometric (or vice versa)
- Miscounting the number of steps
- Not checking both differences AND ratios to identify pattern type