Figure Series — AAI ATC Reasoning Lesson

Before you start

Learning objectives and outcomes

Every figure series is a pattern-finding exercise wearing a picture instead of a number sequence. The method is identical to a number series: find the rule from the first few terms, confirm it holds throughout, then extend it by one more step.

Objective 1Recognise the common types of change: rotation, reflection, added or removed elements, and shading.

Objective 2Isolate a single rule by comparing consecutive figures pairwise, not the series as a whole at once.

Objective 3Confirm a candidate rule against every figure in the series before applying it to find the answer.

Objective 4Handle series where two independent changes happen together, each following its own pattern.

Outcome APredict the next figure in a rotation-based or shading-based series confidently and quickly.

Outcome BSeparate two simultaneous rules and track each one independently.

Subtopic 1

The kinds of change a figure series uses

Almost every figure series is built from one or two of a small number of standard transformations, applied consistently at each step.

The standard transformations

Rotation by a fixed angle · Shading that moves, grows, or alternates
Elements added or removed one at a time · A shape growing, shrinking, or multiplying in count

Once you notice which of these is happening, the rest of the series becomes predictable rather than mysterious.

Step 1

→

Step 2

→

Step 3

→

?

Figure 13.1 — A pure rotation series A triangle rotating 90 degrees clockwise at each step across three panels, with a fourth blank panel marked with a question mark for the student to complete by continuing the same rotation. Upload image here

✈ AAI ATC relevance — figure series questions appear in most reasoning sections, usually two to three per shift

Memory trick — "Name the change before you hunt for the answer"

Say out loud, even mentally, exactly what is changing — "rotating 90° clockwise each time" or "one more dot added each step." A vague sense of "something is turning" is not enough to extend the series reliably.

EasyATC Pattern

In a figure series, if a shape rotates 90° clockwise between each pair of consecutive figures, after four steps it will have rotated a total of:

Four steps of 90° each total 360°, which brings the shape back to exactly where it started. Recognising this lets you skip ahead in a long series without redrawing every step.

ModerateATC Pattern

A series shows a square with an increasing number of dots inside it: 1 dot, then 2, then 3. How many dots should appear in the next figure?

The rule is simply "add one dot each step," so the fourth figure should contain 4 dots.

Subtopic 2 · highest yield

Finding the rule, pair by pair

Do not try to see the whole series' pattern in one look. Compare only the first two figures, form a hypothesis, and then test it against the next pair.

The three-step process

1. Compare figure 1 to figure 2 and note every difference
2. Check that the same difference explains figure 2 to figure 3
3. Apply the confirmed rule one more time to predict the answer

If the rule from step 1 does not survive step 2 unchanged, the real rule is something else, and it is better to find that out on the second figure than to guess on the last one.

Figure 13.2 — Testing a rule pair by pair A four-panel figure series with the transformation between each consecutive pair labelled underneath in small text, showing how the same single rule — for example a shaded half moving one position clockwise — is checked and confirmed across all three visible transitions before being applied to find the fourth figure. Upload image here

Memory trick — "Confirm twice before you predict"

A rule that only explains one pair of figures might be a coincidence. A rule that explains two consecutive pairs is far more likely to be the real pattern, and is safe to extend.

Worked example

A series shows a circle with a small shaded triangle attached, appearing first at the top, then at the right, then at the bottom. What should the fourth figure show?

Compare figure 1 to figure 2: the shaded triangle has moved from the top position to the right position, a quarter turn clockwise around the circle.
Compare figure 2 to figure 3: the triangle has moved from the right position to the bottom position, again a quarter turn clockwise. The rule survives the second comparison.
The confirmed rule is "the shaded triangle moves one quarter turn clockwise at each step."
Applying it once more moves the triangle from the bottom position to the left position, which is the expected fourth figure.

EasyATC Pattern

Why should a candidate rule be checked against at least two consecutive pairs before being used to predict the answer?

Many different rules could explain a single change. Only a rule that holds across at least two consecutive comparisons is trustworthy enough to extend to the missing figure.

ModerateATC Pattern

A shaded dot on a clock face moves from the 12 position to the 3 position, then from the 3 position to the 6 position. Where should it appear next?

The dot moves a quarter turn clockwise each time: 12 to 3, then 3 to 6, so the next quarter turn takes it to the 9 position.

Subtopic 3

When two rules run at the same time

Harder questions layer two independent changes on top of each other — for example, a shape that rotates and gains an extra line at every step. Track each rule separately rather than trying to see both at once.

Split, then recombine

Track the rotation on its own. Track the added element count on its own.
Apply both confirmed rules together to build the final answer.

Treating the two changes as one confused pattern is what makes these questions feel harder than they are. Separated, each one is exactly as simple as a single-rule series.

Figure 13.3 — Two independent rules layered together A four-panel series of an arrow shape that both rotates 45 degrees clockwise at each step and gains one additional short tick mark along its shaft at each step, with the rotation and the tick count each labelled separately beneath the figures to show the two rules being tracked independently. Upload image here

Memory trick — "One rule per hand"

Imagine tracking the rotation with one hand and the added element with the other. Working out both separately and only combining them at the very end avoids the confusion of trying to hold two changing things in mind simultaneously.

HardATC Pattern

A series shows an arrow rotating 45° clockwise at each step while also gaining one extra tick mark at each step, starting with one tick. How many ticks should the fourth figure have, and by how much will the arrow have rotated in total from the first figure?

Track the two rules separately. The tick count rule is "add one each step," starting from 1, so the fourth figure has 1 + 3 = 4 ticks. The rotation rule is "45° clockwise each step," and from the first to the fourth figure that is three steps of 45°, totalling 135°.

ModerateATC Pattern

Why is it recommended to track two simultaneous rules separately rather than together?

Once separated, each individual pattern is no harder than a one-rule series. The apparent difficulty of a two-rule question comes entirely from trying to see both changes at once.

Exam strategy

Five tips that hold in the AAI ATC hall

Name the changePut the pattern into words before trying to extend it.

Compare pairs, not the whole seriesWork figure by figure, not by staring at all of them together.

Confirm twiceA rule that fits only one pair may be a coincidence.

360° means back to startUseful for skipping ahead in long rotation series.

Split simultaneous rulesTrack each independent change on its own, then combine at the end.

Watch for a broken stepOccasionally one figure in the middle deliberately breaks the pattern as a distractor — check every step, not just the first two.

Quick revision

Chapter summary sheet

Core ideaFind the single rule linking each figure to the next, then extend it once more.

Standard changesRotation, shading, added or removed elements, growing or shrinking.

MethodCompare pairwise, confirm the rule survives a second comparison, then predict.

Full rotationFour 90° steps, or eight 45° steps, return a shape to its start.

Two rules at onceTrack each independently; only combine them for the final answer.

Verify fullyCheck the rule against every given figure, not just the first pair.

↓ Free download — Figure Series question PDF

Real drawn series covering rotation, shading, added elements and combined rules, with a full answer key. Print it, solve it, keep it.

Download the free PDF Join our live classes — extremely affordable

End of chapter

Comprehensive assessment

Multiple choice questions on method and concept. Full visual practice with real drawn series is in the downloadable PDF above.

Multiple choice questions

1. Name four standard kinds of change used to build a figure series.

2. If a shape rotates 90° clockwise each step, how many steps return it to its original orientation?

3. What is the first step in finding the rule behind a figure series?

4. Why must a candidate rule be checked against more than one pair of figures?

5. A square gains one more dot at each step, starting with 2 dots. How many dots appear in the fourth figure?

6. A shaded section on a circle moves a quarter turn clockwise each step. Describe where it will be after three steps from the top.

7. What should you do when a figure series appears to have two changes happening at once?

8. Why is tracking two simultaneous rules separately easier than tracking them together?

9. What is the purpose of checking a rule against every given figure rather than stopping after two?

10. An arrow rotates 45° and gains one tick per step, starting at 0° and 1 tick. Describe the fourth figure.

Learning objectives and outcomes

The kinds of change a figure series uses

The standard transformations

Finding the rule, pair by pair

The three-step process

When two rules run at the same time

Split, then recombine

Five tips that hold in the AAI ATC hall

Chapter summary sheet

↓ Free download — Figure Series question PDF

Comprehensive assessment

Multiple choice questions

Name the rule, confirm it twice, then extend it — that is the whole chapter.