Number sequence test: 20 questions with answers

Look at the first two terms. How far did the series move from one to the next?

This is a constant-gap series. Early on the gaps are +2, +2; check the rest, then move one place further.

1. Each term is the one before plus the same fixed amount.
2. The first gaps are +2, +2, so the step is 2.
3. The list ends 11, 13, so the next term is 13 + 2 = 15.

Now find it among the options.

Answer: A. 15.

• A 15✓ AnswerThe correct one is option A: 15.
• B 14Option B is one too few. The rule gives a number right next to it.
• C 17Option C is one step too far along the series.
• D 16Option D lands near the answer but is one too many. The last calculation is close but not exact.

Rather than the gaps, look at how the terms relate in pairs. Test your idea on a second pair.

The ratio of a term to the one before it is 3 for 5 → 15. Check that it holds for the later pairs.

1. The gaps are not the clue here; the multiplier is.
2. It is 3, as 5 → 15 shows, and it stays 3.
3. After 405, 1215, the next term is 3645, since 1215 × 3 = 3645.

Now find it among the options.

Answer: C. 3645.

• A 2565Option A comes from a pattern in the final terms alone. It breaks on the earlier ones.
• B 2025Option B just extends the final step. Look at the earlier steps: they are not all the same size.
• C 3645✓ AnswerThe correct one is option C: 3645.
• D 765Option D comes from following every other term, which does not lead to the next term.

This list of 7 terms may hold two separate runs of numbers. Find where each run goes.

Two series take turns. Odd positions give 1, 6; even positions start 44, 41. Find each step, then pick the series that is next.

1. Split the list by position.
2. Odd positions start 1, 6; even positions start 44, 41.
3. The turn that is due belongs to the even-position series (44, 41, 38), and its own step gives 38 − 3 = 35.
4. So the missing term is 35.

Now find it among the options.

Answer: A. 35.

• A 35✓ AnswerOption A is correct: 35.
• B -6Option B copies the last jump once more. A rule that fits the whole list gives a different term.
• C 36Option C is close, yet one too many. Recheck the final calculation.
• D -55Option D suits the last few terms. A rule must fit every term, and this one does not.

Pick the fourth term. Try to explain it using the terms before it, then test the fifth.

Test the previous two terms against the next one. Early on, 7 + 9 = 16, but the third term is 15. Is the extra the same for 9, 15, 23?

1. Check the rule on 9, 15, 23: the first two, plus an extra of −1, make the third.
2. Apply it at the end of 37, 59: 37 + 59 − 1 = 95.

Now find it among the options.

Answer: C. 95.

• A 81Option A copies the last jump once more. A rule that fits the whole list gives a different term.
• B 59Option B continues every other term at a fixed gap; the rule for every term gives another number.
• C 95✓ AnswerThe answer is option C, which is 95.
• D 89Option D matches a local pattern near the end, but the same rule fails at the start.
• E 96Option E is one too many against the true next term, so the final step was slightly off.

Some terms climb fast and some creep. Sort the 7 terms into the two kinds.

The terms alternate between a multiplying half (2, 4) and a fixed-step half (30, 27). Check each, then see whose turn is next.

1. Each half has its own rule.
2. The multiplying half starts 2, 4 and the fixed-step half starts 30, 27.
3. The turn that is due belongs to the fixed-step half (30, 27, 24).
4. So 24 − 3 = 21.

Now find it among the options.

Answer: D. 21.

• A 20Option A is one too few against the true next term, so the final step was slightly off.
• B 8Option B copies the last jump once more. A rule that fits the whole list gives a different term.
• C -16Option C comes from a pattern in the final terms alone. It breaks on the earlier ones.
• D 21✓ AnswerOption D is correct: 21.
• E 22Option E lands near the answer but is one too many. The last calculation is close but not exact.