Geometric Sequences Trivia Questions Quiz

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| By Courtney Frank

Courtney Frank

Community Contributor

Quizzes Created: 44 | Total Attempts: 15,764

Questions: 5 | Attempts: 389 | Updated: Mar 22, 2023

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Questions and Answers

1.

Determine which sequence is geometric.
- A.
  
  -16, -13, -10, -7, ...
- B.
  
  1, 1, 2, 3, 5, ...
- C.
  
  -3, -6, -12, -24, ...
- D.
  
  5, 7, 9, 11, ...
Correct Answer
C. -3, -6, -12, -24, ...

Explanation
The sequence -3, -6, -12, -24, ... is geometric because each term is obtained by multiplying the previous term by a constant factor of -2.

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2.

Find the fifth term in a sequence in which the first term is 3 and the common ratio is -4.
- A.
  
  60
- B.
  
  -3072
- C.
  
  -729
- D.
  
  768
Correct Answer
D. 768

Explanation
The given sequence is a geometric sequence with a first term of 3 and a common ratio of -4. To find the fifth term, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1). Plugging in the values, we get a5 = 3 * (-4)^(5-1) = 3 * (-4)^4 = 3 * 256 = 768. Therefore, the fifth term in the sequence is 768.

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3.

What is the 7th term of the geometric sequence:
- A.
  
  -48
- B.
  
  192
- C.
  
  3072
- D.
  
  -12288
Correct Answer
B. 192

Explanation
The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by a constant factor. In this case, the common ratio is -4. To find the 7th term, we can use the formula for the nth term of a geometric sequence: an = a1 * r^(n-1). Plugging in the values, we get a7 = -48 * (-4)^(7-1) = -48 * (-4)^6 = -48 * 4096 = -196,608. However, this answer does not match any of the given options. Therefore, the correct answer is not available or there may be an error in the question.

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4.

The 15th term of a geometric sequence is 32,768. Which choice shows the possible first term and the possible common ratio?
- A.
  
  2, 2
- B.
  
  4, 3
- C.
  
  15, 4
- D.
  
  8, -4
Correct Answer
A. 2, 2

Explanation
In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio. To find the 15th term, we start with the first term and multiply it by the common ratio 14 times. Given that the 15th term is 32,768, it means that the first term multiplied by the common ratio 14 times equals 32,768. The only choice that satisfies this condition is 2 as the first term and 2 as the common ratio.

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5.

Find the next two terms of the geometric sequence 50, 40, 32, ...
- A.
  
  24, 15768
- B.
  
  25.6, 20.48
- C.
  
  26, 22128
- D.
  
  28.5, 25.52
Correct Answer
B. 25.6, 20.48

Explanation
The given geometric sequence is obtained by multiplying each term by 0.8. To find the next term, we multiply the last term (32) by 0.8, resulting in 25.6. To find the term after that, we again multiply by 0.8, giving us 20.48. Therefore, the next two terms of the geometric sequence are 25.6 and 20.48.

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Current Version
Mar 22, 2023

Quiz Edited by
ProProfs Editorial Team
Jan 20, 2015

Quiz Created by
Courtney Frank

Geometric Sequences Trivia Questions Quiz

Determine which sequence is geometric.

Find the fifth term in a sequence in which the first term is 3 and the common ratio is -4.

What is the 7th term of the geometric sequence:

The 15th term of a geometric sequence is 32,768. Which choice shows the possible first term and the possible common ratio?

Find the next two terms of the geometric sequence 50, 40, 32, ...