Number Series: Practice Set 2
Number Series: Practice Set 2 is a second practice round on 11+ verbal reasoning number series, moving beyond the single constant difference or constant multiplier of the introductory topic into series built from two combined operations, series where the pattern differs between odd and even terms, and sequences involving square numbers.
Method
- Write down the difference or the ratio between each consecutive pair of numbers before guessing a rule from only the first two terms.
- Check first whether a single operation, a constant add, subtract, multiply or divide, explains every gap in the series.
- If a single operation does not fit every gap, test whether two operations are combined, such as doubling a term and then adding a fixed number.
- If the series still does not fit, check whether the odd-position terms and the even-position terms each follow their own separate, simpler rule.
- Watch for a term that is a square number, since these appear more often in this deeper set than in the introductory topic.
- Once you have confirmed the rule against every gap you can check, apply it once more to the final term to find the missing number.
Worked example
Find the next number: 1, 3, 9, 27, 81, ( ? )
- Find the ratio between each pair of consecutive terms: 3/1=3, 9/3=3, 27/9=3, 81/27=3.
- The ratio is constant at 3, so the rule is multiply by 3 each time.
- Apply the rule to the last term: 81x3=243.
- Final answer: 243.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find the next number: 5, 11, 23, 47, 95, ( ? )Show answer
Answer: 191 (each term is doubled and then 1 is added)
Q2Find the next number: 1, 4, 9, 16, 25, ( ? )Show answer
Answer: 36 (the series is the square numbers in order: 1, 4, 9, 16, 25, 36)
Q3Find the next number: 160, 80, 40, 20, 10, ( ? )Show answer
Answer: 5 (divide by 2 each time)
Q4Find the next number: 2, 30, 4, 27, 6, 24, ( ? )Show answer
Answer: 8 (two series are woven together; the odd positions 2, 4, 6 add 2 each time, giving 8 next; the even positions 30, 27, 24 subtract 3 each time)
Q5Find the next number: 3, 8, 18, 38, 78, ( ? )Show answer
Answer: 158 (each term is doubled and then 2 is added)
Q6Find the next number: 10, 17, 31, 59, 115, ( ? )Show answer
Answer: 227 (each term is doubled and then 3 is subtracted: 10x2-3=17, 17x2-3=31, and so on)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find the next number in this series and identify the rule you used: 7, 14, 28, 56, 112, ( ? ) A) 168 B) 196 C) 200 D) 224 E) 210.
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Find the next number in this series and show your working: 6, 9, 15, 27, 51, ( ? ) A) 75 B) 87 C) 93 D) 99 E) 105.
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Find the next number in this series: 3, 4, 7, 11, 18, 29, ( ? ) A) 36 B) 42 C) 47 D) 51 E) 58.
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Free printable worksheet
Want more practice on paper? Download the number series: practice set 2 worksheet pack - 11 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 6 of 11+ Verbal Reasoning Workbook 2, the whole course as one free printable PDF.
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