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
Write the next two terms of the sequence 5, 8, 11, 14, …
Write down the term-to-term rule for 20, 17, 14, 11, …
Find the nth term of the sequence 4, 7, 10, 13, …
Find the nth term of 6, 11, 16, 21, …
The nth term of a sequence is 4n − 1. Find the 10th term.
Find the nth term of 2, 5, 8, 11, … and use it to find the 50th term.
Is 30 a term of the sequence with nth term 4n + 1?
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
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