Algebra, Sequences and Patterns Depth Set 2
Algebra, Sequences and Patterns Depth Set 2 continues the blended skill from the first set, combining 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. Both skills rely on spotting and describing a consistent relationship between numbers, which is why 11+ papers test them together.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a sequence, compare consecutive terms first to find the term-to-term rule, checking whether the difference stays constant or itself changes by a constant amount.
- Use the term-to-term rule to extend the sequence in either direction, as far as the question requires.
- For a position-to-term, or nth term, rule, test it against at least two terms already known before relying on it for an unknown term.
- For a function machine, apply the operations in the order given to move from input to output, and apply the inverse operations in reverse order to move from output back to input.
- For a simple equation, undo the operations on the unknown one at a time, working in the reverse order to how they were applied.
- Check any rule or solution by substituting a value back into the original problem and confirming it produces a result that matches.
Worked example
The first term of a sequence is 5. Each term after that is found by doubling the previous term and then adding 3. Find the first four terms of the sequence.
- The first term is given: 5.
- Find the second term: 5 x 2 = 10, then 10 + 3 = 13.
- Find the third term: 13 x 2 = 26, then 26 + 3 = 29.
- Find the fourth term: 29 x 2 = 58, then 58 + 3 = 61.
- The first four terms are 5, 13, 29, 61.
Practice questions
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Q1Find the next two terms in this sequence: 5, 9, 13, 17, ...Show answer
Answer: 21 and 25
Q2The nth term of a sequence is 4n - 1. Find the 6th term.Show answer
Answer: 23
Q3A function machine takes an input, multiplies it by 3, then subtracts 5, to give an output of 22. What was the input?Show answer
Answer: 9
Q4Solve for x: x - 7 = 15.Show answer
Answer: 22
Q5Solve for x: 4x + 5 = 33.Show answer
Answer: 7
Q6Find the missing term in this sequence: 3, 7, 13, 21, [], 43.Show answer
Answer: 31
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 6n - 4. (a) Find the 7th term. (b) Which term of the sequence is equal to 62?
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A function machine has two steps: first add 6 to the input, then multiply the result by 2, giving an output of 34. What was the original input?
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The first term of a sequence is 7. Each term after that is found by subtracting 2 and then doubling the result. Find the fourth term of the sequence, showing each step.
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Free printable worksheet
Want more practice on paper? Download the algebra, sequences and patterns depth set 2 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 14 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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