Finding Common Ratio

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

• 6

• 3

• 2

• 4

Answer explanation

The bacteria growth in the petri dish follows a geometric sequence where each term is multiplied by 2. Thus, the common ratio of this sequence is 2, making it the correct choice.

Tags

CCSS.HSF.BF.A.2

The rule for finding a_n of a geometric sequence is a_n = 10(2)^n-1 _{What is the common ratio(r) of the sequence?}

• ²

• ¹⁰

• ²⁰

• 2ⁿ

Answer explanation

In a geometric sequence, the common ratio (r) can be found from the formula a_n = a_1 * r^(n-1). Here, a_1 = 10 and r = 2. Thus, the common ratio is 2.

Tags

CCSS.HSF.BF.A.2

What kind of sequence is illustrated below?

400, 200, 100, 50, 25, ...

• Arithmetic, d = ½

• Geometric, r = ½

• Neither

Answer explanation

The sequence is geometric because each term is obtained by multiplying the previous term by 1/2 (r = ½). For example, 400 × 1/2 = 200, 200 × 1/2 = 100, and so on.

Tags

CCSS.HSF.BF.A.2

Given the sequence: 2, 6, 18, 54, what is the common ratio?

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• 5

Tags

CCSS.HSF.BF.A.2

What is the common ratio of the geometric sequence: 5, 15, 45, 135?

• 1

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• 4

Tags

CCSS.HSF.BF.A.2

Determine the common ratio for the sequence: 7, 14, 28, 56.

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• 4

Tags

CCSS.HSF.BF.A.2

Find the common ratio of the sequence: 10, 30, 90, 270.

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• 5

Tags

CCSS.HSF.BF.A.2

Determine the common ratio for the sequence: 8, 24, 72, 216.

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Tags

CCSS.HSF.BF.A.2

Find the common ratio of the sequence: 3, 12, 48, 192.

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Tags

CCSS.HSF.BF.A.2

What is the common ratio of the sequence: 9, 27, 81, 243?

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• 5

Tags

CCSS.HSF.BF.A.2