Worksheets · Foundation and Higher

The nth term of a linear sequence

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Calculator · 2 marks
(a) The nth term of a sequence is 7n $-$ 4, where the first term has n = 1. Work out the tenth term. (2)
Question 2Non-calculator · 4 marks
Pattern 1 of a matchstick sequence uses 4 matches, pattern 2 uses 7 and pattern 3 uses 10. Each pattern adds the same number of matches.
(a) Find an expression for the number of matches in pattern n. (2)
(b) Sam has 100 matches. What is the largest pattern number he can make? (2)
Question 3Non-calculator · 5 marks
Sequence A has $n$ th term $3n + 2$ . Sequence B has $n$ th term $47 - 2n$ . Sequence C has $n$ th term $4n + 1$ .
(a) Sequences A and B have one term in the same position that is equal. Find the value of that term. (2)
(b) Find the three smallest numbers that are terms of both sequence A and sequence C. (3)

Answers and marks

(a) $66$

(a) $3n+1$

(b) $33$

(a) $29$

(b) $5, 17, 29$

P1 Listing enough terms of both sequences to find a common term, or finding that 5 is in both.
P1 Recognising that common terms go up by 12 (the LCM of 3 and 4).
A1 The correct answer, $5, 17, 29$ .

The nth term of a linear sequence

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