EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Non-Linear Sequences
Non-linear sequences · Algebra · Lesson 6 of 7 · 14 marks · 25 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [1 mark]
Here are the first six terms of a Fibonacci sequence: 1, 1, 2, 3, 5, 8. Write down the next term.
Question 2 NON-CALCULATOR [2 marks]
Here are the first four terms of a geometric sequence: 2, 6, 18, 54. (a) Write down the next term. (b) Work out the 6th term.
Question 3 NON-CALCULATOR · HIGHER [3 marks]
The first two terms of a Fibonacci-type sequence are a and b. The 3rd term is 7 and the 5th term is 18. Find the values of a and b.
Question 4 NON-CALCULATOR · HIGHER [3 marks]
Find an expression for the nth term of the quadratic sequence 3, 9, 19, 33, 51, ...
Question 5 NON-CALCULATOR · HIGHER [3 marks]
Find an expression for the nth term of the quadratic sequence 0, 5, 12, 21, 32, ...
Question 6 NON-CALCULATOR · HIGHER [2 marks]
The first term of a geometric sequence is √3 and the common ratio is √3. Show that the 5th term is 9√3.
Answers
Check your answer only once you have written one.
Question 1 [1 mark]
13
▸ 13 B1
Question 2 [2 marks]
(a) 54 × 3 = 162 (b) 162 × 3 = 486
▸ (a) 162 B1
▸ (b) 486 B1
Question 3 [3 marks]
The terms are a, b, a + b, a + 2b, 2a + 3b. So a + b = 7 and 2a + 3b = 18. Doubling the first: 2a + 2b = 14, so b = 4 and a = 3.
▸ Terms written in terms of a and b, at least to a + 2b M1
▸ a + b = 7 and 2a + 3b = 18 M1
▸ a = 3 and b = 4 A1
Question 4 [3 marks]
First differences 6, 10, 14, 18; second difference 4, so 2n². 2n² gives 2, 8, 18, 32, 50; the sequence minus 2n² is 1, 1, 1, 1, 1. nth term 2n² + 1.
▸ Second difference of 4, or 2n² seen M1
▸ Sequence minus 2n² found, e.g. 1, 1, 1, ... M1
▸ 2n² + 1 A1
Question 5 [3 marks]
First differences 5, 7, 9, 11; second difference 2, so n². n² gives 1, 4, 9, 16, 25; the sequence minus n² is −1, 1, 3, 5, 7, with nth term 2n − 3. nth term n² + 2n − 3.
▸ Second difference of 2, or n² seen M1
▸ −1, 1, 3, 5, 7 or 2n − 3 found M1
▸ n² + 2n − 3 A1
Question 6 [2 marks]
5th term = √3 × (√3)⁴ = √3 × 9 = 9√3
▸ √3 × (√3)⁴, or the terms √3, 3, 3√3, 9, 9√3 listed M1
▸ Correct working showing 9√3 A1