Geometric Sequences worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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3 marks
Here are the first four terms of a geometric sequence.
\(4,\ 16,\ 64,\ 256\)
(a)Write down the common ratio of the sequence.
(b)Work out the next two terms of the sequence.
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4 marks
A geometric sequence begins
\(10,\ 30,\ 90,\ 270,\ \dots\)
(a)Find an expression, in terms of \(n\), for the \(n\)th term of this sequence.
(b)Work out the 8th term of the sequence.
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3 marks
Here are the first four terms of a geometric sequence.
\(168,\ 84,\ 42,\ 21\)
(a)Write down the common ratio of the sequence.
(b)Find the fifth term of the sequence.
Give your answer as a fraction.
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5 marks
The number of greenfly in a greenhouse is multiplied by 3 every week.
At the start there are 30 greenfly.
(a)Work out how many greenfly there will be after 2 weeks.
(b)Work out after how many weeks the number of greenfly first becomes greater than 7,300.
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4 marks
Here are the first four terms of a geometric sequence.
\(9,\ -27,\ 81,\ -243\)
(a)State the common ratio of the sequence.
(b)Work out the seventh term of the sequence.
(c)Is the 84th term of this sequence positive or negative?
Explain your answer.
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3 marks
Here are the first four terms of a geometric sequence.
\(6,\ 30,\ 150,\ 750\)
(a)State the common ratio of the sequence.
(b)Work out the next two terms of the sequence.
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4 marks
A geometric sequence begins
\(2,\ 4,\ 8,\ 16,\ \dots\)
(a)Find an expression, in terms of \(n\), for the \(n\)th term of this sequence.
(b)Work out the 9th term of the sequence.
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3 marks
Here are the first four terms of a geometric sequence.
\(432,\ 144,\ 48,\ 16\)
(a)Write down the common ratio of the sequence.
(b)Find the fifth term of the sequence.
Give your answer as a fraction.
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5 marks
The number of greenfly in a greenhouse is multiplied by 2 every week.
At the start there are 7 greenfly.
(a)Work out how many greenfly there will be after 4 weeks.
(b)Work out after how many weeks the number of greenfly first becomes greater than 900.
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4 marks
Here are the first four terms of a geometric sequence.
\(4,\ -8,\ 16,\ -32\)
(a)Write down the common ratio of the sequence.
(b)Find the seventh term of the sequence.
(c)Is the 98th term of this sequence positive or negative?
Explain your answer.
Answers
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(a) \(4\)
(b) \(1,024,\ 4,096\) -
(a) \(10 \times 3^{n-1}\)
(b) \(21,870\) -
(a) \(\frac{1}{2}\)
(b) \(\frac{21}{2}\) -
(a) \(270\)
(b) \(6\ \text{weeks}\) -
(a) \(-3\)
(b) \(6,561\)
(c) It is negative, because 84 is even and the terms alternate: every odd-numbered term is positive and every even-numbered term is negative. -
(a) \(5\)
(b) \(3,750,\ 18,750\) -
(a) \(2 \times 2^{n-1}\)
(b) \(512\) -
(a) \(\frac{1}{3}\)
(b) \(\frac{16}{3}\) -
(a) \(112\)
(b) \(8\ \text{weeks}\) -
(a) \(-2\)
(b) \(256\)
(c) It is negative, because 98 is even and the terms alternate: every odd-numbered term is positive and every even-numbered term is negative.