EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Linear Sequences
Linear sequences · Algebra · Lesson 5 of 7 · 12 marks · 20 minutes
Name Date
Answer all questions. Show your working. Questions 1 to 3 are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
Here are the first five terms of a sequence: 5, 9, 13, 17, 21. Find an expression, in terms of n, for the nth term of the sequence.
Question 2 NON-CALCULATOR [2 marks]
Is 99 a term of the sequence 5, 9, 13, 17, 21, ...? You must give a reason for your answer.
Question 3 NON-CALCULATOR [2 marks]
Find an expression for the nth term of the sequence 30, 26, 22, 18, ...
Question 4 CALCULATOR [3 marks]
The diagram shows the first three patterns in a sequence made from matchsticks. Pattern 1 uses 4 matchsticks, pattern 2 uses 7 and pattern 3 uses 10. Jack has 150 matchsticks. What is the largest pattern number he can make?
Question 5 CALCULATOR [3 marks]
Sequence A has nth term 3n + 5. Sequence B has nth term 50 − 2n. For which value of n are the nth terms of the two sequences equal, and what is that term?
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
4n + 1
▸ 4n + 1 B2
▸ 4n + k, where k ≠ 1 B1
Question 2 [2 marks]
4n + 1 = 99 gives n = 24.5, which is not a whole number, so 99 is not a term. (The terms go 97, 101.)
▸ 4n + 1 = 99, or listing terms to 97 and 101 M1
▸ No, with a correct reason C1
Question 3 [2 marks]
34 − 4n
▸ 34 − 4n B2
▸ −4n + k, where k ≠ 34 B1
Question 4 [3 marks]
The nth pattern uses 3n + 1 matchsticks. 3n + 1 ≤ 150, so 3n ≤ 149 and n ≤ 49.67. The largest pattern is pattern 49 (it uses 148 matchsticks).
▸ 3n + 1, or the difference of 3 used P1
▸ 3n + 1 = 150 or 3n + 1 ≤ 150, or 49.6… seen P1
▸ 49 A1
Question 5 [3 marks]
3n + 5 = 50 − 2n, so 5n = 45 and n = 9. The term is 3 × 9 + 5 = 32.
▸ 3n + 5 = 50 − 2n M1
▸ n = 9 A1
▸ 32 A1