Lemmara logoLemmaraWorked solution

0580/22 Oct/Nov 2022, Question 6: Quadratic and Cubic Sequences

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Find the next two terms of the sequence 27, 26, 23, 18, 11, and complete a table giving the nth term for sequences A (3, 10, 17, 24, 31) and B (2, 11, 26, 47, 74).

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Find the next two terms after 27, 26, 23, 18, 11.

  1. 1Differences: −1, −3, −5, −7, so next differences are −9, −11
  2. 211 − 9 = 2, 2 − 11 = −9
  3. 3Next two terms: 2, −9

Answer2, −9

Part (b) · 4 marks

Complete the table by writing the nth term for sequence A and for sequence B.

  1. 1A: common difference 7, so 7n + c; 7 × 1 + c = 3 gives c = −4
  2. 2Sequence A: 7n − 4
  3. 3B: first differences 9, 15, 21, 27; second differences 6, so 3n²
  4. 43n²: 3, 12, 27, 48, 75; sequence B is 1 less each time
  5. 5Sequence B: 3n² − 1

Answer| Sequence A | 7n − 4 | | Sequence B | 3n² − 1 |

Stuck on a step? Read the free lesson: Quadratic and Cubic Sequences

Practise more quadratic and cubic sequences questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on quadratic and cubic sequences

Also searched as: 0580/22/O/N/22 · 0580_w22_qp_22 · 0580 w22 22 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.