Algebra and Sequences: Practice Set 5
Algebra and Sequences: Practice Set 5 is a mixed practice set combining early algebra, such as function machines and simple equations, with number sequences, such as term-to-term and position-to-term rules. Papers pair these two skills because both test whether a student can spot and use a general rule rather than performing one specific calculation.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a function machine or equation, identify what operations have been applied to the unknown, then reverse them in the opposite order to find its value.
- For a simple equation such as 3x+4=19, isolate the unknown one step at a time, undoing addition or subtraction before multiplication or division.
- For a substitution question, replace each letter with its given value before doing any arithmetic, following the correct order of operations.
- For a sequence, find the term-to-term rule first by comparing consecutive terms, looking for a common difference or ratio.
- If a sequence has a constant difference, the position-to-term rule takes the form 'n times the difference, then adjust'; test it against the first term to find the adjustment.
- Extend a sequence by repeatedly applying the term-to-term rule, or find a distant term using the position-to-term rule instead of counting on by hand.
- Check any algebra answer by substituting it back into the original equation or sequence rule.
Worked example
The nth term of a sequence is given by the rule 4n - 3. Find the 6th term, then find which term of the sequence equals 33.
- Find the 6th term by substituting n = 6: 4 x 6 - 3 = 24 - 3 = 21.
- To find which term equals 33, set 4n - 3 = 33.
- Add 3 to both sides: 4n = 36.
- Divide both sides by 4: n = 9.
- Check: 4 x 9 - 3 = 36 - 3 = 33, which matches, so it is the 9th term.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Solve: x + 7 = 15.Show answer
Answer: x = 8
Q2Solve: 5x = 35.Show answer
Answer: x = 7
Q3Find the missing number in the function machine: input, then x3, then +4, gives an output of 19.Show answer
Answer: Reverse: 19 - 4 = 15, then 15 / 3 = 5, so the input is 5.
Q4If a=4 and b=3, find the value of 2a+3b.Show answer
Answer: 2 x 4 + 3 x 3 = 8 + 9 = 17.
Q5Find the next term: 7, 12, 17, 22, ...Show answer
Answer: Add 5 each time: 22 + 5 = 27.
Q6A sequence has nth term 40 - 4n. Write the first three terms and explain how you can tell, without listing them all, that 0 will appear in the sequence.Show answer
Answer: 36, 32, 28. The terms fall by 4 each time from 36, and 36 is a multiple of 4, so every term is a multiple of 4 and the sequence reaches 0 exactly. Setting 40 - 4n = 0 gives n = 10, so 0 is the 10th term.
Q7Solve: 2x - 5 = 11.Show answer
Answer: 2x = 16, so x = 8.
Q8Find the term-to-term rule for the sequence 100, 90, 80, 70, ...Show answer
Answer: Subtract 10 each time.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Solve the equation 3(x + 2) = 21 to find the value of x, showing each step.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A sequence begins 5, 9, 13, 17, ... (a) Find the nth term rule for this sequence. (b) Use it to find the 20th term.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the algebra and sequences: practice set 5 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 17 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on algebra and sequences: practice set 5, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.