Finding the Common Ratio of a Geometric Sequence

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.

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Find the common ratio for the geometric sequence.

10, 40, 160, 640, ...

• 2

• 4

• 10

• 1/2

Answer explanation

To find the common ratio, divide the second term by the first: 40/10 = 4. Check with the next terms: 160/40 = 4 and 640/160 = 4. Thus, the common ratio is 4.

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CCSS.HSF.BF.A.2

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Given the sequence, what is the common ratio?

• 4

• 2

• 1

• 1/2

Answer explanation

The common ratio in a geometric sequence is found by dividing any term by the previous term. If the sequence shows that each term is multiplied by 2 to get the next, then the common ratio is 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.

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Find the common ratio: 64, -16, 4, -1, ...

• r = -8

• r = -1/4

• r = -4

• r = 4

Answer explanation

To find the common ratio, divide each term by the previous one. For example, -16/64 = -1/4, 4/-16 = -1/4, and -1/4 = -1/4. Thus, the common ratio is r = -1/4.

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CCSS.HSF.BF.A.2

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What is the common ratio in the geometric sequence 72, 36, 18, 9...

• 1/3

• 1/2

• 2

• 3

Answer explanation

In a geometric sequence, the common ratio is found by dividing any term by the previous term. Here, 36/72 = 1/2, 18/36 = 1/2, and 9/18 = 1/2. Thus, the common ratio is 1/2.

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Is this sequence Arithmetic, Geometric, or Neither?

{14, 22, 30, 38, .. }

• Arithmetic, d = 8

• Geometric, r = ⅛

• Neither

Answer explanation

The sequence {14, 22, 30, 38, ..} is arithmetic because the difference between consecutive terms is constant: 22-14 = 8, 30-22 = 8, and 38-30 = 8. Thus, it has a common difference (d) of 8.

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CCSS.HSF.BF.A.2

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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.

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Which formula is used to find the equation for geometric sequences?

• f(x) = a + d

• f(x) = a * r

• f(x) = a + d(n-1)

• f(x) = a * r^n-1

Answer explanation

The formula f(x) = a * r^(n-1) is used for geometric sequences, where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number. This correctly represents the nth term of a geometric sequence.

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

• $10

• $300

• $162

• $416

Answer explanation

Daisy receives $2 on her 1st birthday. Each year, the amount triples: 1st: $2, 2nd: $6, 3rd: $18, 4th: $54, 5th: $162. Therefore, on her 5th birthday, she will receive $162.

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