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Year 9 · Practice

Sequences & the nth Term — Year 9 Practice Questions

Work through these Year 9 practice questions on sequences and the nth term. Try each one before revealing the worked solution.

Questions

1
[2 marks] Easy Continuing

Write the next two terms of the sequence 5, 8, 11, 14, …

2
[1 marks] Easy Term-to-term

Write down the term-to-term rule for 20, 17, 14, 11, …

3
[2 marks] Medium nth term

Find the nth term of the sequence 4, 7, 10, 13, …

4
[2 marks] Medium nth term

Find the nth term of 6, 11, 16, 21, …

5
[2 marks] Medium Using nth term

The nth term of a sequence is 4n − 1. Find the 10th term.

6
[3 marks] Hard Using nth term

Find the nth term of 2, 5, 8, 11, … and use it to find the 50th term.

7
[3 marks] Hard Membership

Is 30 a term of the sequence with nth term 4n + 1?

8
[3 marks] Hard Decreasing

Find the nth term of the decreasing sequence 19, 16, 13, 10, …

Answers & Worked Solutions

Question 1 Solution

Step 1: The common difference is 3.

Step 2: 14 + 3 = 17, 17 + 3 = 20.

Answer: 17, 20

Question 2 Solution

Step 1: Each term is 3 less than the one before.

Step 2: So the rule is subtract 3.

Answer: Subtract 3

Question 3 Solution

Step 1: The common difference is 3, giving 3n.

Step 2: 3×1 = 3, and we need 4, so add 1: 3n + 1.

Answer: 3n + 1

Question 4 Solution

Step 1: Common difference 5 gives 5n.

Step 2: 5×1 = 5, need 6, so add 1: 5n + 1.

Answer: 5n + 1

Question 5 Solution

Step 1: Substitute n = 10: 4×10 − 1.

Step 2: = 40 − 1 = 39.

Answer: 39

Question 6 Solution

Step 1: Common difference 3 gives 3n; 3×1 = 3, need 2, subtract 1 → 3n − 1.

Step 2: 50th term: 3×50 − 1 = 149.

Answer: 3n − 1; 149

Question 7 Solution

Step 1: Set 4n + 1 = 30, so 4n = 29 and n = 7.25.

Step 2: n is not a whole number, so 30 is not a term.

Answer: No

Question 8 Solution

Step 1: The common difference is −3, giving −3n.

Step 2: −3×1 = −3, need 19, so add 22: 22 − 3n.

Answer: 22 − 3n

Build strong foundations in Sequences & the nth Term

A free trial class with Teacher Rig helps your Year 9 child master Sequences & the nth Term now — so IGCSE Maths feels familiar, not frightening, later.

Next step: IGCSE

Heading toward IGCSE? See how Sequences & the nth Term develops in IGCSE Algebra and Graphs (Cambridge 0580)