Sequences and Early Algebra: Practice Set 4
Sequences and Early Algebra: Practice Set 4 covers finding and using term-to-term and position-to-term rules for number sequences, alongside early algebra skills such as function machines, simple one-step and two-step equations, and substituting numbers into a word formula. These are staple 11+ topics because they test logical, step-by-step thinking without needing GCSE-level algebraic notation.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a term-to-term rule, work out what is done to each term to get the next one by comparing consecutive terms.
- For a position-to-term rule, look at how the term value relates to its position number (1st, 2nd, 3rd...), checking whether it is a multiple of the position plus or minus a fixed amount.
- For a function machine, apply each operation in the order shown to go forwards, or apply the inverse operations in reverse order to go backwards from an output.
- For a simple equation such as 3x + 4 = 19, undo the operations in reverse order: subtract first, then divide.
- For substitution, replace each letter with its given number carefully, then follow the normal order of operations to work out the value.
- Always check your answer by substituting it back into the original rule, equation or formula to confirm it works.
Worked example
The nth term of a sequence is given by 4n - 3. Find the first three terms of the sequence, and state whether 41 is a term in this sequence.
- Substitute n = 1: 4 x 1 - 3 = 1, so the first term is 1.
- Substitute n = 2: 4 x 2 - 3 = 5, so the second term is 5.
- Substitute n = 3: 4 x 3 - 3 = 9, so the third term is 9.
- To check 41, set 4n - 3 = 41 and solve: add 3 to both sides to get 4n = 44, then divide by 4 to get n = 11.
- Since n = 11 is a whole number, 41 is a term in the sequence, it is the 11th term.
Practice questions
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Q1Find the next two terms of the sequence 5, 9, 13, 17, ...Show answer
Answer: 21, 25 (the term-to-term rule is add 4)
Q2The nth term of a sequence is 2n + 6. Find the 5th term.Show answer
Answer: 16 (2 x 5 + 6)
Q3A function machine multiplies a number by 3, then adds 5. If the output is 26, what was the input?Show answer
Answer: 7 (undo: 26 - 5 = 21, then 21 / 3 = 7)
Q4Solve the equation 5x - 2 = 18.Show answer
Answer: x = 4 (add 2 to get 5x = 20, then divide by 5)
Q5If a = 6 and b = 4, work out the value of 3a - b.Show answer
Answer: 14 (3 x 6 = 18, 18 - 4 = 14)
Q6A sequence starts 40, 34, 28, 22, ... Describe the term-to-term rule.Show answer
Answer: Subtract 6 each time
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The nth term of a sequence is 5n + 2. (a) Find the first term and the tenth term of the sequence. (b) Is 92 a term in this sequence? Show your working and explain your answer.
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A function machine takes a number, subtracts 7, then divides the result by 3, to give an output of 8. Using inverse operations, find the original input number, showing each step.
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Free printable worksheet
Want more practice on paper? Download the sequences and early algebra: practice set 4 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 16 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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