AQA · Mathematics · 8300
GCSE Maths: Sequences: nth term
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Sequences: nth term (Corbettmaths Video 288), 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 the general form of an arithmetic sequence's nth term?
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an + b, where a is the common difference and b is a constant.
In the sequence 7, 10, 13, 16, 19, the common difference is ?.
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3
If a sequence has nth term 6n + 3, what is the 1st term?
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9 (substitute n = 1: 6(1) + 3 = 9)
How can you check if a number is a term in the sequence with nth term 6n + 3?
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Solve 6n + 3 = that number for n. If n is a positive integer, it's a term; otherwise it's not.
For the sequence 1, 5, 9, 13, 17, the nth term is ?.
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4n − 3
What is the first term of the sequence with nth term n² + 3?
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4 (substitute n = 1: 1² + 3 = 4)
For the sequence 10, 7, 4, 1, −2, what is the common difference?
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−3 (each term decreases by 3)
The nth term of the sequence 10, 7, 4, 1, −2 is ?.
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13 − 3n
If the nth term of a sequence is 3n − 2, which term equals 70?
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The 24th term (solve 3n − 2 = 70: 3n = 72, n = 24)
For the sequence with nth term 4n − 7, what is the difference between the 150th and 151st terms?
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4 (the common difference, which is the coefficient of n)
If the last term of the sequence 4n − 7 is 393, how many terms are in the sequence?
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100 terms (solve 4n − 7 = 393: 4n = 400, n = 100)
What is the nth term of the sequence 1, 4, 9, 16, 25, ...?
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n²
What is the nth term of the sequence 3, 6, 11, 18, 27, ...?
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n² + 2
What is the nth term of the arithmetic sequence 30, 25, 20, 15, 10, ...?
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35 - 5n
What is the nth term of the arithmetic sequence 9, 17, 25, 33, ...?
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8n + 1
What is the nth term of the sequence 2, 2.5, 3, 3.5, 4, ...?
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0.5n + 1.5 (or 1.5 + 0.5n)
If the 4th term of a linear sequence is 26 and the 6th term is 32, what is the nth term?
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3n + 14
What is the nth term of the sequence 1/12, 5/23, 9/34, 13/45, 17/56, ...?
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(4n - 3)/(11n + 1)
What is the nth term of the fraction sequence 2/3, 3/5, 4/7, 5/9, ...?
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(n + 1)/(2n + 1)
For the sequence with nth term 150 - 4n, which term is the first negative term?
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The 38th term (when 150 - 4n < 0, so n > 37.5, meaning n = 38 is the first negative)
What is the nth term of sequence A: 4, 9, 14, 19, ...?
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5n - 1
What are the first three terms of the sequence with nth term (n + 1)(n + 3)?
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8, 15, 24 (obtained by substituting n = 1, 2, 3 into (n + 1)(n + 3))
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