Algebra, Sequences and Patterns Depth
Algebra, Sequences and Patterns Depth combines number sequences, finding a term-to-term or position-to-position rule, with early algebra, function machines and simple one-step or two-step equations, since both skills rely on spotting and describing a consistent relationship between numbers. 11+ papers test this blended skill because it separates children who can only follow a worked routine from those who can identify the underlying rule and apply it to a new case.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a sequence, find the term-to-term rule first by comparing consecutive terms, checking whether the difference is constant or changes by a constant amount each time.
- Once you have the term-to-term rule, use it to extend the sequence forwards, or backwards, as far as the question needs.
- For a position-to-position rule, the nth term, test your rule against at least two terms you already know before trusting it, since a rule that works for one term by coincidence is not reliable.
- For a function machine, work through the operations in the order given to go from input to output, and apply the inverse operations in reverse order to work from output back to input.
- For a simple equation, undo the operations applied to the unknown, one at a time, in the reverse order to how they were applied, to isolate the unknown.
- Check your final rule or equation solution by substituting a specific value back in and confirming it gives a result that matches the question.
Worked example
The first term of a sequence is 4. Each term after that is found by multiplying the previous term by 2 and then subtracting 1. Find the first four terms of the sequence.
- The first term is given: 4.
- Find the second term: 4 x 2 = 8, then 8 - 1 = 7.
- Find the third term: 7 x 2 = 14, then 14 - 1 = 13.
- Find the fourth term: 13 x 2 = 26, then 26 - 1 = 25.
- The first four terms are 4, 7, 13, 25.
Practice questions
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Q1Find the next two terms in this sequence: 3, 7, 11, 15, ...Show answer
Answer: 19 and 23
Q2The nth term of a sequence is 3n + 2. Find the 5th term.Show answer
Answer: 17
Q3A function machine takes an input, multiplies it by 4, then adds 3, to give an output of 27. What was the input?Show answer
Answer: 6
Q4Solve for x: x + 9 = 20.Show answer
Answer: 11
Q5Solve for x: 3x - 4 = 17.Show answer
Answer: 7
Q6Find the missing term in this sequence: 2, 5, 10, 17, [], 37.Show answer
Answer: 26
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The nth term of a sequence is given by 5n - 3. (a) Find the 6th term. (b) Which term of the sequence is equal to 42?
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A function machine has two steps: first subtract 5 from the input, then multiply the result by 3, giving an output of 24. What was the original input?
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Free printable worksheet
Want more practice on paper? Download the algebra, sequences and patterns depth worksheet pack - 10 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 13 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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