Quadratic Sequences

Sample Quadratic Sequences questions

A few of the 36 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 13 marksGrade 4
   Here are the first four terms of a quadratic sequence: 11, 26, 45, 68. Work out an expression for the nth term.
   Show the worked solution

   First differences: 15, 19, 23. Second differences: 4, 4 - constant, confirming a quadratic sequence. M1

   n² coefficient = 4÷2 = 2.

   Subtract 2n² from each term: 11-2=9, 26-8=18, 45-18=27, 68-32=36 - this is 9n. M2

   nth term = 2n² + 9n. A1
2. Question 22 marksGrade 5-6
   The number of seats in each row of a stadium's expanding upper tier, counting outward from the front. Here are the first four terms: 6, 11, 18, 27, ... Work out the next (5th) term of the sequence.
   Show the worked solution

   First differences: 5, 7, 9

   Second difference is constant at 2, so the next first difference is $9 + 2 = 11$

What are the common mistakes in Quadratic Sequences?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Uses the constant second difference directly as the n^2 coefficient instead of halving it

  Used the second difference directly as the coefficient of n^2, forgetting to halve it

• Correctly finds a quadratic nth-term's n^2 coefficient but doesn't go on to find the constant term

  Correctly found the $n^2$ coefficient (3) but didn't go on to find the constant term

• Extends a quadratic sequence using a constant (first) difference instead of the growing second-difference pattern

  Assumed a constant first difference (treated the sequence as arithmetic) instead of using the growing second-difference pattern

Quick answers about Quadratic Sequences

How many Quadratic Sequences practice questions are there?

There are 36 self-marking GCSE Maths questions on Quadratic Sequences, written for AQA, Pearson, OCR across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Quadratic Sequences?

No. You can start practising Quadratic Sequences straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.