AQA · Mathematics · 8300
GCSE Maths: Geometric progressions
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Geometric progressions (Corbettmaths Video 375), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What defines a geometric progression?
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A sequence in which each term is found by multiplying the previous term by a fixed number, the common ratio.
Which of these is a geometric progression: 5,8,11,14; 5,6,11,17; 5,10,20,40; 5,7,11,17?
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5, 10, 20, 40 — each term is multiplied by a common ratio of 2.
What is the next term of the sequence 1, 4, 16, 64, 256?
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1024 — each term is multiplied by 4.
How do you find the common ratio of a geometric progression from two consecutive terms?
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Divide any term by the term before it, e.g. 15 ÷ 5 = 3.
A geometric progression has second term 2 and third term 8. What is its first term?
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0.5 — the ratio is 4, so divide 2 by 4.
What is the third term of the geometric progression 60, 12, …?
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2.4 — the common ratio is 12 ÷ 60 = 1/5.
How do you find the common ratio from the first and third terms of a geometric progression?
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Divide the third term by the first to get r², then square-root (e.g. 48 ÷ 3 = 16, so r = ±4).
What is the sum of the first 5 terms of the geometric sequence 3, 12, …?
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1023 — the terms are 3 + 12 + 48 + 192 + 768.
In a geometric progression, the ninth term is double the tenth term. What is the common ratio?
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1/2 — each term is half the previous one.
What is the formula for the nth term of a geometric progression with first term a and common ratio r?
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a × r^(n−1).
What is the fifth term of the geometric sequence 2, 2√7, 14, 14√7, …?
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98 — the common ratio is √7, and 14√7 × √7 = 98.
The first three terms of a geometric sequence are (x − 15), x and (3x + 20), with x positive. What is x?
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x = 20 — set x² = (x − 15)(3x + 20), giving 2x² − 25x − 300 = 0, so x = 20.
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