EduTest Year 9–10 numerical reasoning: number sequences (10 questions)

Quick Answer

Write the differences between the terms first. If they do not settle into a pattern, look for two sequences woven together, or a rule that combines two operations, then test the rule on every given term before choosing an answer. This page has ten original sequences for EduTest Year 9–10 entry, and every answer shows the tempting rule that fits the first terms and the exact term where it fails.

Who is this practice for, and which EduTest level?

This set is for students in Year 8 or Year 9 preparing for an EduTest scholarship or entrance test for Year 9 or Year 10 entry. "Year 9–10 entry" is our label for this practice and for our Year 9–10 EduTest course. It is not a year band published by EduTest, which tests students at their current year level.

EduTest describes its numerical reasoning section as multiple-choice, 30 minutes long, and covering series, matrices, arithmetical reasoning and deduction (EduTest information for parents, read on 15 October 2026). The page does not publish a question count, and we do not claim these ten items match the difficulty of a real paper. If your child is preparing for Year 7 entry, start with the EduTest hub and its year-level table instead.

How do we find the rule in a harder sequence? Two worked sequences

Worked sequence 1: 4, 30, 7, 26, 10, 22, ?

1. Write the differences. +26, −23, +19, −16, +12. They do not settle, so do not trust a single rule yet.
2. Split by position. Positions 1, 3, 5 give 4, 7, 10. Positions 2, 4, 6 give 30, 26, 22.
3. Name each rule. The first goes up by 3. The second goes down by 4.
4. Answer. The 7th term continues the first sequence: 10 + 3 = 13.

The tempting rule: "add 26, subtract 23, repeat". It fits 4, 30, 7 exactly. It predicts 33 as the 4th term, but the 4th term is 26. The rule breaks at term 4.

Worked sequence 2: 2, 5, 11, 23, 47, ?

1. Write the differences. +3, +6, +12, +24. Each difference doubles.
2. Look for one step that makes the doubling. Doubling the term and adding 1 gives 2 → 5 → 11 → 23 → 47.
3. Test every term. 2 × 2 + 1 = 5, 5 × 2 + 1 = 11, 11 × 2 + 1 = 23, 23 × 2 + 1 = 47.
4. Answer. 47 × 2 + 1 = 95.

The tempting rule: "the differences go up by 3 each time (+3, +6, +9)". It fits 2, 5, 11. It predicts 20 as the 4th term, but the 4th term is 23. The rule breaks at term 4.

The questions

Work in pencil. For each one, write the differences, name your rule, and check it against every given term before you choose. Answers are on a separate sheet at the end.

Question 1

5, 20, 8, 17, 11, 14, 14, ?

What is the 8th term?

• A. 14
• B. 17
• C. 11
• D. 29

Question 2

5, 40, 10, 35, 20, 30, 40, ?

What is the 8th term?

• A. 25
• B. 60
• C. 35
• D. 10

Question 3

2, 5, 7, 8, 12, 11, 17, ?

What is the 8th term?

• A. 22
• B. 16
• C. 20
• D. 14

Question 4

3, 5, 9, 17, 33, ?

What is the next term?

• A. 49
• B. 65
• C. 51
• D. 66

Question 5

2, 4, 10, 28, 82, ?

What is the next term?

• A. 136
• B. 140
• C. 244
• D. 246

Question 6

1, 2, 3, 6, 7, 14, 15, ?

What is the 8th term?

• A. 30
• B. 16
• C. 31
• D. 29

Question 7

4, 5, 8, 13, 20, 29, ?

What is the next term?

• A. 38
• B. 39
• C. 56
• D. 40

Question 8

1, 2, 6, 15, 31, ?

What is the next term?

• A. 47
• B. 56
• C. 54
• D. 95

Question 9

1/2, 3/4, 7/8, 15/16, 31/32, ?

What is the next term?

• A. 49/64
• B. 1
• C. 63/64
• D. 47/64

Question 10

2, 3, 5, 9, ?, 33, 65

What is the missing term?

• A. 11
• B. 13
• C. 15
• D. 17

Answers with the failed-rule check

Each answer gives the rule that works for every term, then the tempting rule that fits the first terms and the term where it breaks. Every wrong option comes from a rule like that one.

Question 1 answer: C, 11

True rule: two interleaved sequences. Positions 1, 3, 5, 7 go up by 3 (5, 8, 11, 14). Positions 2, 4, 6, 8 go down by 3 (20, 17, 14, 11). The 8th term is 11.

Tempting rule: alternately add 15 and subtract 12. It fits 5, 20, 8 but predicts 23 as the 4th term; the 4th term is 17. It breaks at term 4. Followed on, it gives option D (29). Option B (17) adds 3 to both sequences, and option A (14) repeats the 7th term.

Question 2 answer: A, 25

True rule: two interleaved sequences. Positions 1, 3, 5, 7 double (5, 10, 20, 40). Positions 2, 4, 6, 8 go down by 5 (40, 35, 30, 25). The 8th term is 25.

Tempting rule: alternately add 35 and subtract 30. It fits 5, 40, 10 but predicts 45 as the 4th term; the 4th term is 35. It breaks at term 4. Followed on, it gives option D (10). Option B (60) doubles the second sequence as well, and option C (35) adds 5 where the rule subtracts it.

Question 3 answer: D, 14

True rule: two interleaved sequences. Positions 1, 3, 5, 7 go up by 5 (2, 7, 12, 17). Positions 2, 4, 6, 8 go up by 3 (5, 8, 11, 14). The 8th term is 14.

Tempting rule: the differences fall by 1 each step (+3, +2, +1, +0, −1). It fits 2, 5, 7, 8, so it survives four terms. It predicts 8 as the 5th term, but the 5th term is 12. It breaks at term 5. Option A (22) is the next term of the other sequence, in 9th place. Option B (16) adds 5 to both sequences. Option C (20) adds 3 to the last term.

Question 4 answer: B, 65

True rule: double the term and subtract 1. Check: 3 × 2 − 1 = 5, 5 × 2 − 1 = 9, 9 × 2 − 1 = 17, 17 × 2 − 1 = 33, so 33 × 2 − 1 = 65. The differences double (2, 4, 8, 16), which is the same rule seen from the other side.

Tempting rule: the differences go up by 2 (+2, +4, +6). It fits 3, 5, 9 but predicts 15 as the 4th term; the 4th term is 17. It breaks at term 4. Followed on, it gives option C (51). Option D (66) doubles without subtracting 1, and option A (49) repeats the last difference of 16.

Question 5 answer: C, 244

True rule: multiply by 3 and subtract 2. Check: 2 × 3 − 2 = 4, 4 × 3 − 2 = 10, 10 × 3 − 2 = 28, 28 × 3 − 2 = 82, so 82 × 3 − 2 = 244.

Tempting rule: the differences go up by 4 (+2, +6, +10). It fits 2, 4, 10 but predicts 20 as the 4th term; the 4th term is 28. It breaks at term 4. Followed on, it gives option B (140). Option D (246) multiplies by 3 and forgets to subtract 2, and option A (136) repeats the last difference of 54.

Question 6 answer: A, 30

True rule: alternately multiply by 2 and add 1, starting with multiply by 2. Check: 1 × 2 = 2, 2 + 1 = 3, 3 × 2 = 6, 6 + 1 = 7, 7 × 2 = 14, 14 + 1 = 15, so 15 × 2 = 30.

Tempting rule: add 1 each time. It fits 1, 2, 3 but predicts 4 as the 4th term; the 4th term is 6. It breaks at term 4. Followed on, it gives option B (16). Option C (31) does both steps at once, 15 × 2 + 1, and option D (29) adds the last difference of 14.

Question 7 answer: D, 40

True rule: add the odd numbers in turn: +1, +3, +5, +7, +9, then +11. So 29 + 11 = 40.

Tempting rule: the differences multiply by 3 (+1, +3, +9). It fits 4, 5, 8 but predicts 17 as the 4th term; the 4th term is 13. It breaks at term 4. Followed on, it gives option C (56). Option A (38) repeats the last difference of 9, and option B (39) adds 10, raising the difference by 1 where it has been rising by 2.

Question 8 answer: B, 56

True rule: add the square numbers in turn: +1, +4, +9, +16, then +25. So 31 + 25 = 56.

Tempting rule: the differences multiply by 4 (+1, +4, +16). It fits 1, 2, 6 but predicts 22 as the 4th term; the 4th term is 15. It breaks at term 4. Followed on, it gives option D (95). Option C (54) raises the last difference by 7 instead of by 9, and option A (47) repeats the last difference of 16.

Question 9 answer: C, 63/64

True rule: each term is the gap to 1 halved again. The denominator doubles and the numerator is always one less than the denominator, so the gaps are 1/2, 1/4, 1/8, 1/16, 1/32, then 1/64. The next term is 63/64.

Tempting rule: the numerators go up by 2, then 4, then 6 over a doubling denominator. It fits 1/2, 3/4, 7/8 but predicts 13/16 as the 4th term; the 4th term is 15/16. It breaks at term 4. Continuing it gives option A (49/64). Option D (47/64) repeats the last numerator difference of 16. Option B (1) adds the last difference of 1/32 again and so reaches 1, which the terms approach but never reach.

Question 10 answer: D, 17

True rule: the differences double: +1, +2, +4, +8, +16, +32. So the missing term is 9 + 8 = 17, and 17 + 16 = 33 and 33 + 32 = 65 confirm it.

Tempting rule: prime numbers in order. It fits 2, 3, 5 but predicts 7 as the 4th term; the 4th term is 9. It breaks at term 4. Followed on, it gives option A (11) for the missing place. Option B (13) repeats the difference of 4, and option C (15) adds 6, raising the differences by 2 each time.

What mistake patterns should we look for?

• Stopping at the first rule that fits. Every question here is built so that the first terms fit a wrong rule. Ask your child to check the rule on every given term, not just the first three.
• Continuing the wrong sequence. In interleaved sequences, the next position belongs to one chain only. Ask which chain the asked-for term sits in before calculating.
• Applying one step to both chains. Options like 17 in Question 1 and 60 in Question 2 come from giving both chains the same rule.
• Repeating the last difference. Questions 4, 5, 7, 8 and 9 all offer it. If the differences have been changing, they will keep changing.
• Taking part of a combined rule. Option D in Question 5 multiplies by 3 and forgets the subtraction. Test both steps on the first pair of terms.

Can my child write a sequence that fools the first guess?

Ask your child to write a six-term sequence with a two-part rule, for example "add 3, then double", and a tempting rule that fits the first three terms and fails at the fourth. Then swap with someone and have them find both. Writing the failed rule is the harder half, and it is what stops a student settling at three terms.

Self-check: list the six terms, write the differences, and confirm the true rule on every term. Then write the tempting rule's prediction for the 4th term and circle the term where the two disagree.

What should we do after this set?

• If the tempting rule caught your child on more than three questions, redo those questions tomorrow and write the failed rule before the true one.
• Read the EduTest exam format guide to see how numerical reasoning sits among the other sections, and the EduTest practice resources guide for other free material.
• EduTest publishes its own practice tests; check the page for the levels it offers.
• The free mock tests need a free classroom account. Use one when your child is ready for a timed sitting.
• For structured practice across all EduTest sections, see what the Year 9–10 entry EduTest course includes. Confirm your child's entry year and your school's test provider before buying.

Sources and review

Official source (checked 2026-10-15): EduTest, information for parents: the numerical reasoning section is multiple-choice and 30 minutes long, and covers series, matrices, arithmetical reasoning and deduction. The page gives no question count for it.

Where the questions came from: all ten sequences and both worked sequences are original Braintree Coaching Australia material written for this page. None is taken from an EduTest or third-party paper. Every sequence was checked by script: the true rule reproduces every shown term and the answer, the tempting rule fits the terms before the breaking term and fails at it, and every wrong option is the output of a named failed rule.

Author: James Rush, content writer, Braintree Coaching Australia.

Review status: the answers have not yet been solved blind by a reviewer outside the team, and a named teacher review has not yet been recorded. If an answer looks wrong to you, please tell us.

Last updated: 2026-10-15.