How to Choose the Option That Continues a Pattern

A “choose the option that continues the pattern” problem asks you to infer a rule from a short sequence, then use that rule to select the next item. But without the sequence, picture, and answer choices, there is no particular option to identify. The method below works for number sequences and many visual-pattern questions.

What makes a pattern rule convincing?

A finite list can usually be continued in many different ways. For example, the numbers $2, 4, 6$ could continue as $8$ by adding $2$, but a more complicated rule could make the next number something else. In ordinary multiple-choice puzzles, the intended rule is generally the simplest consistent rule: one that explains all the items without adding unnecessary exceptions.

“Simple” depends on the kind of puzzle. For numbers, check arithmetic changes. For pictures, check properties such as the number of objects, their location, direction, color, or rotation. Do not settle on a rule just because it predicts the final item; it must also fit the earlier ones.

A step-by-step method

1. Write down the observable features. For numbers, list the terms. For shapes, describe what changes: for example, “one dot moves clockwise” or “the triangle alternates between filled and unfilled.”
2. Compare neighbors. Look at the difference, ratio, count, orientation, or position from one item to the next.
3. Check for a repeating or alternating rule. Some sequences use a two-step cycle, such as “add 2, then add 5.” Visual puzzles often alternate between two transformations.
4. Test your rule on every given item. If it fails even once, revise it rather than ignoring the mismatch.
5. Predict the next item, then compare it with the options. If no option matches, reconsider the rule or check whether you overlooked a feature.

Worked example: a number sequence

Suppose the sequence is $3, 7, 11, 15, ?$, with options $18, 19, 20, 21$.

Calculate the differences between adjacent terms:

$$\begin{aligned} 7-3&=4,\\ 11-7&=4,\\ 15-11&=4. \end{aligned}$$

The same change, $+4$, appears each time. Applying it once more gives $15+4=19$, so the matching option is 19. The check matters: the proposed rule explains every transition, not just the last one.

If the differences are not constant, take a second look at the differences themselves. For example, in $1, 4, 9, 16, ?$, the first differences are $3, 5, 7$. Those increase by $2$, so the next difference is $9$, giving $16+9=25$. Equivalently, these are the squares $1^2, 2^2, 3^2, 4^2$, so the next term is $5^2=25$.

Worked example: a visual pattern

Imagine three panels. Each panel contains one arrow, and the arrow points up, right, then down. The direction turns $90$ degrees clockwise each time. The next arrow should point left. If the options show several arrows, choose the left-pointing one.

Before deciding, inspect other features too. If the arrow also changes color or the number of arrows increases, those may be independent parts of the rule. A good prediction should account for all visible changes, not merely the most noticeable one.

Common mistakes

• Using only the last two items. A rule that fits the final transition may contradict an earlier transition. Check the whole sequence.
• Assuming every number pattern uses addition. Try differences, ratios, alternating operations, squares, or another simple structure when addition does not fit.
• Ignoring position or orientation in diagrams. A shape may stay the same while rotating, moving, or changing order.
• Overcomplicating the rule. A complicated formula can fit a short list by coincidence. Prefer a familiar, economical rule when it explains all the evidence.
• Forcing an answer from the choices. Options can help confirm a prediction, but selecting the most plausible-looking choice first can bias your reasoning.

When more than one answer seems possible

Short patterns are sometimes underdetermined: two simple rules may fit all the displayed items but predict different next ones. In that case, use the conventions of the puzzle and the answer choices to find the most likely intended rule, but recognize that the information may not determine a unique continuation. To select a specific option, you need the actual sequence or image and the available choices; the general instruction alone does not specify an answer.