PSHS NCE Patterns, Sequences, and Number Relationships Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Patterns, Sequences, and Number Relationships

Spot how numbers change, find the rule, and predict what comes next without checking every possible answer.

Arithmetic patternsGrowing patternsMissing termsQuick Fire + Mastery

LearnFast MethodExamplesTry With MePracticeQuick FireMastery

MY STATUS

Patterns, Sequences, and Number Relationships

Not yet started on this browser.

NOT STARTED

START HERE

Ask: what changes each time?

Sequence = numbers arranged in an order that follows a rule.

Same difference:
5, 9, 13, 17
Add 4 each time.

Same factor:
3, 6, 12, 24
Multiply by 2 each time.

Changing difference:
2, 5, 9, 14
Add 3, then 4, then 5.

Alternating rule:
4, 7, 14, 17, 34
+3, ×2, +3, ×2.

FAST METHOD

Check the gaps first

1. Subtract neighboring terms. Are the differences the same?
2. If not, check whether the differences themselves follow a pattern.
3. Check simple multiplication or division.
4. If neither works, test an alternating rule.
5. Use the simplest rule that explains every term.

WORKED EXAMPLES

Six common pattern types

1. Same difference

12, 17, 22, 27, ?

Add 5 each time.

32

2. Same factor

2, 6, 18, 54, ?

Multiply by 3 each time.

162

3. Growing differences

4, 7, 11, 16, 22, ?

Differences are +3, +4, +5, +6. Next is +7.

29

4. Alternating operations

5, 10, 12, 24, 26, ?

×2, +2, ×2, +2, so next is ×2.

52

5. Square numbers

1, 4, 9, 16, 25, ?

These are 1², 2², 3², 4², 5².

36

6. Missing middle term

8, 13, ?, 23, 28

Add 5 each time.

18

TRY WITH ME

Use the gaps

Find the next number:

3, 7, 12, 18, 25, ?

1. Find the differences: +4, +5, +6, +7.
2. The difference increases by 1 each time.
3. Next difference is +8.

33

COMMON TRAPS

Watch out for these

Guessing from only the first two terms.
The rule must fit the whole sequence.

Missing an alternating pattern.
Try checking odd-position and even-position steps separately.

Forcing a complicated rule.
Entrance tests usually reward the simplest consistent pattern.

Ignoring changing differences.
If the first differences are not equal, inspect how they change.

REGULAR PRACTICE

Build the skill

QUICK FIRE

Can you spot the rule fast?

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency.

NEED HELP?

Can't see the pattern yet?

Send Teacher Abi the sequence. I can help you test the differences, factors, and alternating rules without giving away the method too early.

Message Teacher Abi

PSHS NCE REVIEW PATH

Choose your next step

Next competency: Counting, Data, and Probability

Previous: Measurement and Unit ConversionPSHS NCE Student Hub