Question 1 Easy
A geometric sequence starts 3, 12, 48. What is the next term?
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Answer: 192
- The ratio is 4.
- 48 x 4.
- Method (1): The ratio is 4.
- Accuracy (1): Answer 192
Geometric sequences practice questions with answers
A second set of geometric sequences questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
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Question 2 Easy
A geometric sequence starts 1000, 500, 250. What is the next term?
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Answer: 125
- The ratio is 1/2.
- Half of 250.
- Method (1): The ratio is 1/2.
- Accuracy (1): Answer 125
Question 3 Medium
Work out the 5th term of the geometric sequence 81, 27, 9, ...
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Answer: 1
- The ratio is 1/3.
- 81 x (1/3)^4.
- Method (1): The ratio is 1/3.
- Accuracy (1): Answer 1
Question 4 Medium
The numbers 4, x, 36 are consecutive terms of a geometric sequence and x is positive. Find x.
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Answer: 12
- x squared is 4 x 36 = 144.
- x = 12.
- Method (1): x squared is 4 x 36 = 144.
- Accuracy (1): Answer 12
Question 5 Hard
500 pounds is invested at 3% compound interest each year. How much is it worth after 4 years, to the nearest penny? Give the number only.
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Answer: 562.75
- The multiplier is 1.03.
- 500 x 1.03^4.
- Method (1): The multiplier is 1.03.
- Accuracy (1): Answer 562.75
Question 6 Hard
A car is worth 8000 pounds and loses 20% of its value each year. What is it worth after 3 years, in pounds?
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Answer: 4096
- The multiplier is 0.8.
- After 3 years it is the 4th term, 8000 x 0.8^3.
- Method (1): The multiplier is 0.8.
- Accuracy (1): Answer 4096
Exam-style question
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Exam-style question 13 marks
2000 pounds is invested at 4% compound interest each year. Work out the value after 5 years to the nearest penny. Give the number only.
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Answer: 2433.31
- The multiplier is 1.04.
- 2000 x 1.04^5.
- The value is 2433.31.
- Method (1): Uses the multiplier 1.04
- Method (1): Works out 2000 x 1.04^5
- Accuracy (1): Gives 2433.31
Quick checks
Short one-step questions. Pick an option before you open the answer.
Check 1
How do you find the common ratio of a geometric sequence?
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Divide any term by the term before it. Divide any term by the term before it.
Check 2
What is the difference between arithmetic and geometric sequences?
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Arithmetic adds the same number each time. Geometric multiplies by the same number each time. Arithmetic adds the same number each time. Geometric multiplies by the same number each time.
Check 3
What is the nth term of a geometric sequence?
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a x r^(n-1), where a is the first term and r is the common ratio. a x r^(n-1), where a is the first term and r is the common ratio.
Check 4
Why is the power n - 1 and not n?
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The first term has no r in it. Each step to the next term adds one more factor of r. The first term has no r in it. Each step to the next term adds one more factor of r.
Check 5
How do you check an nth term formula?
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Put n = 1. It must give the first term. Put n = 1. It must give the first term.
Check 6
What does a ratio between 0 and 1 do to the terms?
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They shrink towards zero. They shrink towards zero.
Check 7
What does a negative ratio do to the terms?
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The signs alternate between positive and negative. The signs alternate between positive and negative.
Check 8
How do you find the term before a given term?
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Divide by the common ratio. Divide by the common ratio.
Check 9
Two terms are 3 places apart. What do you get by dividing the later by the earlier?
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r cubed. Take the cube root to find r. r cubed. Take the cube root to find r.
Check 10
If x is the middle of three consecutive terms, what is x squared?
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The first term times the third term. The first term times the third term.
Check 11
What is the ratio for 4% yearly growth?
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What is the ratio for 4% yearly growth: 1.04. 1.04.
Check 12
What is the ratio for 20% yearly decay?
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What is the ratio for 20% yearly decay: 0.8. 0.8.
Check 13
Is year 0 or year 1 the first term in a compound interest sequence?
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Year 0, the starting amount, is the first term. Year 0, the starting amount, is the first term.
Check 14
After n years, which term is the value?
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Term n + 1, which is the starting amount times the multiplier to the power n. Term n + 1, which is the starting amount times the multiplier to the power n.
Check 15
What mistake does 5 x 2^n make for the sequence 5, 10, 20?
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It gives 10 at n = 1. The power should be n - 1. It gives 10 at n = 1. The power should be n - 1.
Keep going with Geometric sequences
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