Nth Term Practice Test Worksheets
Nth term questions ask you to turn arithmetic sequences into a formula. This page shows how to spot the common difference, find the 0th term, and choose the correct expression for position n.
For students who can follow number patterns, but need faster and more accurate sequence formula practice.
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The Rules Every Nth Term Question Uses
The worksheets use increasing and decreasing arithmetic sequences in number lists, tables, and short pattern scenarios. These rules cover the method used in the answer keys.
🔍 Rule 1: Find the common difference
Subtract one term from the next. This difference becomes the coefficient of n.
Example: 8, 11, 14, 17 has difference +3, so the formula starts 3n.
⬅ Rule 2: Step back to term 0
The 0th term is found by moving one step before the first term using the same difference.
Example: If term 1 is 8 and the difference is +3, term 0 is 5.
➕ Rule 3: Combine both parts
Write the common difference next to n, then add or subtract the 0th term.
Example: Difference +3 and 0th term 5 gives 3n + 5.
⚠ Rule 4: Keep decreasing signs
For decreasing sequences, the coefficient of n is negative. The 0th term is often larger than term 1.
Example: 46, 40, 34, 28 has difference -6 and 0th term 52, so 52 - 6n.
3 Worked Examples
One straightforward, one table format, and one classic sign trap.
Question: Identify the formula for the nth term of this sequence:
1 3 5 7 9
Worked Method
Step 1: The sequence goes up by 2 each time, so the formula starts with 2n.
Step 2: Go back one step from the first term: 1 - 2 = -1.
Step 3: Combine the parts: 2n - 1.
Answer: 2n - 1.
Tip: Test n = 1. 2(1) - 1 = 1, so the formula matches the first term.
Question: A sequence maps positions to terms as shown below. Which expression represents the nth term?
Position (n): 1 2 3 4 5
Term: 8 11 14 17 20
Worked Method
Step 1: The terms increase by 3, so use 3n.
Step 2: The first term is 8. Step back by 3 to find term 0: 8 - 3 = 5.
Step 3: Add the 0th term to the n part: 3n + 5.
Answer: 3n + 5.
Tip: A table does not change the method. Use the term row to find the difference.
Question: Choose the correct expression for the nth term of the sequence:
46 40 34 28 22
Worked Method
Step 1: The sequence decreases by 6, so the formula starts with -6n.
Step 2: To go back one step before 46, add 6: 46 + 6 = 52.
Step 3: Combine the 0th term and the negative n part: 52 - 6n.
Answer: 52 - 6n.
Tip: Do not write 46 - 6n. That would give 40 when n = 1, not 46.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Nth Term pack contains 90 questions across 3 printable test sets. Students practise arithmetic sequences presented as number lists, tables, and short pattern scenarios, with answer keys included.
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