Questions

1)

Define a geometric sequence.

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2)

Find the next three terms in the following geometric sequence.

1, –2, 4, –8, …

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3)

Find the next three terms in the following geometric sequence.

8, 20, 50, …

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4)

Find the first five terms of the geometric sequence for which:

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5)

Find the first five terms of the geometric sequence for which a₁ = 10 and r = –1.

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6)

Find the 7^th term of the geometric sequence for which a₁ = 5 and r = –2.

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7)

Find the 10^th term of the geometric sequence for that begins 2, 6, 18, …

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8)

Fill in the table for the geometric sequence represented by f (n) = –3 × 2ⁿ^{– 1}

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9)

Use the table to write an explicit formula for the geometric sequence.

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10)

Given the function f (n) = 85 × (2/3)^{n –}¹, state a₁ and r.

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11)

Write the explicit formula for the sequence: 200, 100, 50, 25.

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12)

Using the graph, write the explicit formula for the geometric sequence. Click here to view the graph. (Hint, use points from the graph to make a table.)

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13)

a_n = 3 – (n – 1) × 4

A) arithmetic sequences

B) geometric sequences

C) neither

14)

f (n) = 4 – n

A) arithmetic sequences

B) geometric sequences

C) neither

15)

f (n) = 4 × 3ⁿ^{– 1}

A) arithmetic sequences

B) geometric sequences

C) neither

16)

Explain how to write the function for a geometric sequence given a table of values.

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17)

Use the table below and determine if it is an arithmetic or geometric sequence. Then, write an explicit formula for finding any term in the sequence.

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18)

Jackson is told that he will be given 1 cent for working today. However, for each day he works, he will get double the pay. So, on day 2, he gets 2 cents, on day 3, 4 cents, and so on. Jackson thinks, no way, that’s not much money. But if he agrees, how much will he make on day 20?

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19) A culture of bacteria doubles every 4 hours. If there are 500 bacteria present at the beginning, how many bacteria will there be after 24 hours?

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20)

Explain where the Fibonacci sequence is found in nature.

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21)

What did the most famous Fibonacci problem posed have to do with?

A) deer

B) fish

C) rabbits

D) horses

22)

Consider the following scatterplot. Does it show a linear, quadratic, or exponential function?

A) Linear

B) Quadratic

C) Exponential

D) None, there is no correlation

23)

The following data represents the length of baby as it grows during pregnancy. The average length at various points in the pregnancy is recorded (in inches). Use this data to make a scatterplot and find a best fit line. Give your answer for the best fit line. State which points you used to find the equation of the line.