AQA · Mathematics · 8300
GCSE Maths: Arithmetic progressions
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Arithmetic progressions (Corbettmaths Video 374), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is an arithmetic progression?
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A sequence in which the difference between consecutive terms is constant (the common difference).
Which of these is an arithmetic progression: 3, 6, 12, 24 or 3, 5, 7, 9?
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3, 5, 7, 9 — it has a constant difference of 2. (3, 6, 12, 24 is geometric: it doubles each time.)
What is the next term of the arithmetic sequence 17, 21, 25, 29?
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33 — the common difference is 4, so add 4 to 29.
What are the next three terms of the arithmetic progression −2, 8, …?
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18, 28, 38 — the common difference is 10.
What is the nth term of the arithmetic sequence 2, 7, 12, 17?
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5n − 3. The common difference 5 gives 5n; the first term is 2, and 5 × 1 − 3 = 2.
What is the nth term of the arithmetic sequence 7, 1, −5, −11?
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13 − 6n. The common difference is −6, so the coefficient of n is −6; 13 − 6 × 1 = 7.
In the nth term formula of an arithmetic sequence, what does the coefficient of n equal?
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The common difference between consecutive terms.
How do you show that 380 is not a term of the sequence with nth term 7n + 20?
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Solve 7n + 20 = 380 → n = 360 ÷ 7, which is not a whole number, so 380 is not a term.
Is 68 a term of the arithmetic sequence 9, 13, 17, 21, 25?
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No — every term is odd (nth term 4n + 5), so an even number like 68 cannot appear.
What is the next term of the arithmetic progression 5k, 10k, …?
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15k — the common difference is 5k.
What is the next term of the arithmetic sequence 2a + b, 3a + 6b, 4a + 11b?
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5a + 16b — the common difference is a + 5b.
The 10th term of the arithmetic sequence 2k − 1, 5k + 2, 8k + 5 is ?.
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29k + 26
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