Verbal Reasoning: Sequences Set 5
Verbal Reasoning: Sequences Set 5 is the final and hardest practice round on letter and number series in this collection, covering sequences built from two combined operations at once, such as multiply then add, sequences where each new term depends on adding together the two terms before it, and three separate sequences woven together into a single list rather than only two.
Before you start
Make sure you're comfortable with these topics first:
Method
- Write down the actual gap or the actual ratio between each pair of consecutive terms, rather than only glancing at the numbers, since a two-step rule can look random until it is written out in full.
- Test a single operation first, either a constant addition or subtraction, or a constant multiplication or division, and only move on if none of these fits every gap exactly.
- If a single operation does not fit, test a two-step rule such as multiply by a fixed number then add or subtract a fixed number, checking it against at least three consecutive terms before trusting it.
- Check whether each term is built from the two terms before it, such as adding the previous two terms together, which is a common harder rule that a simple gap check will never reveal.
- If the sequence still does not fit any of these, check whether it is three separate sequences woven together, by comparing every third term rather than every other term.
- Once you have confirmed a rule against every term you can check it against, apply it once more to find the missing term, and check your answer for simple arithmetic slips before choosing it.
Worked example
Find the next number in the sequence: 2, 3, 5, 8, 13, ( ? )
- Check for a constant gap first: 3-2=1, 5-3=2, 8-5=3, 13-8=5, so the gaps are not constant and do not grow by a fixed amount either, meaning a simple addition rule does not fit.
- Notice that each gap, 1, 2, 3, 5, matches an earlier term in the sequence itself, which suggests each new term might be built from the two terms before it rather than from a fixed step.
- Test this idea: 2+3=5, which matches the third term; 3+5=8, which matches the fourth term; 5+8=13, which matches the fifth term.
- Confirm the rule holds for every term you can check, then apply it once more: add the last two given terms, 8+13. Final answer: 21.
Practice questions
Try each question, then tap to reveal the answer.
Q1Find the next number: 3, 7, 15, 31, 63, ( ? )Show answer
Answer: 127 - each term doubles and then adds 1 (3x2+1=7, 7x2+1=15, and so on), so 63x2+1=127.
Q2Find the next letter: A, B, D, H, P, ( ? )Show answer
Answer: F - the shift between letters doubles each time (+1, +2, +4, +8), so the next shift is +16; P(16)+16=32, which wraps round the alphabet to position 6, F.
Q3Find the next number in this sequence, which weaves together three separate simpler sequences: 1, 10, 100, 2, 20, 90, 3, 30, 80, ( ? )Show answer
Answer: 4 - the terms in positions 1, 4 and 7 (1, 2, 3) add 1 each time, so the next term in that pattern is 4.
Q4Find the next number: 4, 7, 11, 18, 29, ( ? ) A) 41 B) 47 C) 45 D) 40 E) 49Show answer
Answer: B) 47 - each term is the sum of the two terms before it (4+7=11, 7+11=18, 11+18=29), so the next term is 18+29=47.
Q5Find the next number: 5, 7, 11, 19, 35, ( ? )Show answer
Answer: 67 - the gap between terms doubles each time (+2, +4, +8, +16), so the next gap is +32, giving 35+32=67.
Q6Find the next letter in this woven sequence, which combines three separate simpler sequences: B, Z, G, D, X, I, F, V, K, ( ? )Show answer
Answer: H - the letters in positions 1, 4 and 7 (B, D, F) move forward 2 places each time, so the next in that pattern is H.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find the next number in this sequence, and state the two-step rule you used: 6, 14, 30, 62, 126, ( ? )
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Nothing ticked yet - 3 available
Find the next letter in this sequence, where each letter's alphabet position is the sum of the two positions before it: A, B, C, E, H, M, ( ? )
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Nothing ticked yet - 4 available
Find the next number in this sequence, which weaves together three separate simpler sequences, and explain how you identified all three: 5, 40, 100, 8, 35, 95, 11, 30, 90, ( ? )
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Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the verbal reasoning: sequences set 5 worksheet pack - 14 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 40 of 11+ Verbal Reasoning Workbook 2, the whole course as one free printable PDF.
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