3.2: Figural Sequences

Introduction to Figural Sequences

While figural matrices require analyzing patterns across grids, figural sequences present a linear progression. In the FBI Special Agent Phase I Test, you will encounter series of images arranged in a single row. The final image (or sometimes a middle image) is missing, and your objective is to select the correct image that logically continues the established pattern.

Figural sequences test sequential logic, working memory, and your ability to track multiple changing variables over time. In a real-world investigative setting, FBI Agents must often reconstruct timelines, tracking how a suspect's behavior, financial transactions, or communications escalate or change sequentially. Mastering figural sequences hones your ability to spot these progressive trends.

Core Mechanics of Pattern Progressions

In a sequence, the rule dictates how one image transforms into the next. To solve these problems efficiently, you must learn to identify the most common transformation types: rotation, movement, size scaling, and structural changes.

Rotational Degrees and Angles

One of the most standard transformations is rotation. Elements within the figure, or the entire figure itself, will spin around a central axis. You must determine both the direction (clockwise or counter-clockwise) and the degree of rotation.

• 45-Degree Rotations: The shape moves half a quadrant. For example, a line pointing North rotates to point North-East.
• 90-Degree Rotations: The shape moves a full quadrant. A line pointing North rotates to point East.
• 180-Degree Rotations: The shape flips to the opposite side. A line pointing North rotates to point South.

Rotations can also follow an increasing or decreasing arithmetic progression. The first rotation might be 45 degrees, the second 90 degrees, and the third 135 degrees. You must constantly measure the "distance" between each step to ensure you aren't missing an escalating pattern.

Movement Along a Path

Often, small elements like dots, squares, or arrows move along the perimeter or interior of a larger shape. For example, a black dot might travel along the corners of a hexagon.

To track movement:

1. Identify the track (is it moving along corners, edges, or freely within a grid?).
2. Determine the increment (does it move one space, two spaces, or does the number of spaces change?).
3. Identify the direction (clockwise or counter-clockwise).

If there are multiple moving elements, they might move in opposite directions or at different speeds. Track them individually. If dot A moves +1 clockwise and dot B moves +2 counter-clockwise, determine the final position of A, eliminate wrong choices, and then delete or calculate the final position of B.

Scaling, Alternation, and Structural Changes

Size Scaling and Proportions

Patterns are not limited to spatial placement; they can also involve changes in size or scale. A shape might systematically grow or shrink. More complex sequences involve relative scaling, where an outer shape shrinks while an inner shape grows, eventually causing the inner shape to engulf the outer one. Pay close attention to the relative proportions of elements as you scan from left to right.

Side Count Increments

A very common FBI SAET structural rule is the side count increment. The primary shape in the sequence changes by adding or subtracting sides.

• Step 1: Triangle (3 sides)
• Step 2: Square (4 sides)
• Step 3: Pentagon (5 sides)
• Step 4: Hexagon (6 sides)

This can be combined with other rules. For instance, a triangle with one dot inside might become a square with two dots, then a pentagon with three dots. The rule is: +1 side, +1 dot.

Alternating and Dual-Track Sequences

Not all sequences follow a simple 1 -> 2 -> 3 -> 4 progression. Some sequences are actually two separate patterns woven together. This is known as an alternating or dual-track sequence. In a 6-item sequence, items 1, 3, and 5 follow one rule, while items 2, 4, and 6 follow a completely different rule.

If you look at a sequence and the changes seem random or chaotic—for example, a shape rotates, then changes color entirely, then rotates again—you are likely looking at an alternating sequence. To solve these, physically or mentally skip every other image. Analyze 1 -> 3 -> 5, deduce the rule, and then analyze 2 -> 4 -> 6 to find the missing piece.

Systematic Approach for Test Day

When confronting figural sequences on the exam, use this structured methodology:

1. The Quick Scan: Look at the entire sequence to get a general feel. Is the overall complexity increasing, decreasing, or fluctuating? Fluctuations often suggest alternating patterns.
2. Isolate and Trace: Just like with matrices, pick one specific element (e.g., the shading, a specific line, the outer shape) and trace its progression across the entire sequence.
3. Map the Rule: Explicitly state the rule in your mind (e.g., "The black triangle moves one corner clockwise, while the white circle moves two corners counter-clockwise").
4. Process of Elimination: Apply the rule for the first element to the final step and look at the answer choices. Cross out any options that do not have that element in the correct state. Often, accurately tracking just one or two elements is enough to eliminate all incorrect options.
5. Double-Check with a Secondary Element: If two answer choices remain, pick a different element that you haven't tracked yet, determine its rule, and use it to break the tie.

Developing an eye for rotational degrees, side counts, and dual-track progressions takes practice. By isolating variables and mapping rules methodically, you will navigate these visual puzzles with the precision required to excel on the SAET.