Geometric Progressions

Concept Quizzes

Geometric Progressions Warmup
Geometric Progressions
Geometric Mean
Geometric Progression Sum
Arithmetic and Geometric Progressions Problem Solving

Challenge Quizzes

Geometric Progressions: Level 1 Challenges
Geometric Progressions: Level 2 Challenges
Geometric Progressions: Level 3 Challenges
Geometric Progressions: Level 4 Challenges

Geometric Progressions Warmup

If $\{a_n\}$ is a geometric progression with $a_1 = 5$ and $a_5 = 80$ , what is the value of $a_3$ ?

20 45 62 25

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by Brilliant Staff

If $a_1, 3, a_3, 12, a_5$ is a geometric progression, which of the following is a possible value of $a_5?$

16.5 18 24 48

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by Brilliant Staff

The geometric mean of the geometric sequence ${2, a_2, a_3}$ is 10. What is the value of $a_3?$

Note. The geometric mean of three numbers $a_1, a_2, a_3$ is $\sqrt[3]{a_1\cdot a_2 \cdot a_3}.$ For example, the geometric mean of $2, 4,$ and $8$ is $\sqrt[3]{2\cdot(4)\cdot8} = \sqrt[3]{64} = 4.$

10 25 50 100

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by Brilliant Staff

$x, y, z^2$ is a geometric progression.
Each of $x, y, z$ are integers.
$x + y + z^2 < 120$ .
Find the largest possible value of $x + y + z^2$ .

116 117 111 112

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by Brilliant Staff

If $a_1, 5, a_3, 45, a_5$ is a geometric progression, which of the following is a possible value of $a_3?$

25 -15

\frac{5}{3}

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by Brilliant Staff

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