Verbal Reasoning: Sequences Set 4
Verbal Reasoning: Sequences Set 4 is a fourth practice round on letter and number series for 11+ verbal reasoning papers, moving on from the growing-gap and woven patterns of the earlier sets into series built from two operations at once, series where every third term follows a different rule, and letter series that must be converted to alphabet positions and wrap around more than once.
Before you start
Make sure you're comfortable with these topics first:
Method
- Convert any letters to their alphabet position (A=1 to Z=26) before looking for a pattern, since counting forward or backward by eye becomes unreliable once a series wraps past Z or below A more than once.
- List the gap between every pair of consecutive terms, and check first whether that gap is constant, since a constant gap is both the commonest rule and the quickest to rule in or out.
- If the gap is not constant, check whether it changes by a fixed amount each time, and separately check whether every third term breaks the pattern set by the other two, which is a common twist in this set.
- If a single addition or subtraction rule does not fit, test whether two operations are combined, such as doubling a term and then subtracting a fixed number.
- For a woven series, split the terms into two separate lists, for example every first and third term against every second and fourth term, and find the rule for each list on its own before combining them again.
- Once the rule is confirmed against every gap you can check in the given series, apply it once more to the final term, handle any wraparound carefully, and match your answer to the given options.
Worked example
Find the number that continues the series: 3, 7, 13, 21, 31, ( ? )
- Find the gap between each pair of consecutive terms: 7-3=4, 13-7=6, 21-13=8, 31-21=10.
- The gaps themselves form their own sequence, 4, 6, 8, 10, which increases by 2 each time.
- The next gap in that pattern is 10+2=12.
- Apply this gap to the last given term: 31+12=43.
- Final answer: 43.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find the next number: 2, 5, 11, 23, 47, ( ? )Show answer
Answer: 95 (each term is doubled then 1 is added: 2x2+1=5, 5x2+1=11, and so on)
Q2Find the next letter: D, G, K, P, ( ? )Show answer
Answer: V (the gap between letters grows by 1 each time: +3, +4, +5, then +6)
Q3Find the next number in this woven series: 5, 20, 9, 16, 13, 12, ( ? )Show answer
Answer: 17 (two series are woven together; the odd positions 5, 9, 13 add 4 each time, giving 17 next; the even positions 20, 16, 12 subtract 4 each time)
Q4Find the next number: 4, 8, 100, 12, 16, 100, 20, ( ? )Show answer
Answer: 24 (every third term is a fixed 100; the remaining terms increase by 4 each time they appear: 4, 8, 12, 16, 20, 24)
Q5Find the next letter: B, C, E, I, ( ? )Show answer
Answer: Q (each letter's alphabet position is doubled then 1 is subtracted to get the next: 2x2-1=3=C, 3x2-1=5=E, 5x2-1=9=I, 9x2-1=17=Q)
Q6Find the next number: 2, 4, 10, 28, 82, ( ? )Show answer
Answer: 244 (each term is multiplied by 3 and then 2 is subtracted: 2x3-2=4, 4x3-2=10, and so on)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find the missing number and state the rule you used: 6, 11, 21, 41, 81, ( ? )
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This question has two parts. Part A: find the next letter in the series H, K, O, T, ( ? ). Part B: find the next number in the series 5, 9, 17, 33, 65, ( ? ).
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Find the next number in this woven series and state both underlying rules: 8, 50, 14, 42, 20, 34, ( ? )
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Free printable worksheet
Want more practice on paper? Download the verbal reasoning: sequences set 4 worksheet pack - 12 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 38 of 11+ Verbal Reasoning Workbook 2, the whole course as one free printable PDF.
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