Questions

Arithmetic Sequences

Define an arithmetic sequence.

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Find the next three terms in the following arithmetic sequence:

2, 13, 24, 35, …

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Find the next three terms in the following arithmetic sequence:

31, 24, 17, 10, …

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Find the first five terms of the sequence for which:

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Find the 29^th term of an arithmetic sequence with a₁ = 2 and d = 5.

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Geometric Sequences

Define a geometric sequence.

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Find the next three terms in the following geometric sequence:

1, –2, 4, –8, …

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Find the next three terms in the following geometric sequence.

8, 20, 50, …

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

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10)

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

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11)

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

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Arithmetic Series

12)

Define an arithmetic series.

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13)

Find the sum of the following series.

1 + 2 + 3 + 4 + … + 97 + 98 + 99 + 100

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14)

Find the sum of the first 50 terms of the following series.

7 + 11 + 15 + … + 199 + 203

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15)

Find the sum of the arithmetic series for which a₁ = 2, a_n = 20, and n = 7.

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16)

Find the sum of the arithmetic series for which a₁ = 58, a_n = –7, and n = 26.

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17)

Given 3 + 7 + 11 + 15 + … find S₂₀

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Geometric Series

18)

Define a geometric series.

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19)

Find the sum of the geometric series for which a = 2, r = –3, and n = 8.

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20)

Find the sum of the geometric series for which a = 160, r = 0.5, and n = 6.

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21)

Find the sum of the first 8 terms of the following geometric series

3 + 6 + 12 + 24 +…

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22)

Find the sum of the first 5 terms of the following geometric series.

512 – 256 + 128 +…

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Word Problems on Sequences and Series

23)

There are 25 rows of seats in the high school auditorium with 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. How many total seats are in the auditorium?

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24)

Contagious diseases can spread quickly. Suppose 3 people are ill during the first week of an epidemic, and each person who is ill spreads the disease to five people by the end of the next week. By the end of the 8^th week of the epidemic, how many people have become ill?

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25)

Jackson’s current salary is $36,000 per year. Each year his salary is 1.04 times the previous year’s salary. What will his salary be in his 5th year?

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26)

A pile of bricks has 93 bricks in the first row, 89 bricks in the second row, 85 bricks in the third row, and so on. How many bricks are there in the 12^th row?

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Binomial Theorem

27)

List the coefficients in the row of Pascal’s triangle corresponding to n = 7.

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28)

Use the Binomial Theorem and Pascal’s Triangle to find the expanded form of the binomial expression.

A) Choice A

B) Choice B

29)

Use the Binomial Theorem and Pascal’s Triangle to find the expanded form of the binomial expression.

A) Choice A

B) Choice B

In the following problems, convert the radian measures to degrees. To enter a degree measure via the keyboard, express the answer in the same format as the sample answer shown below.

Write 98º as 98 degrees.

30)

Solve.

Click here to review the unit content explanation for Circular Trigonometry.

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In the following problem, convert the degree measures to radians. To enter a radian measure via the keyboard, express the answer in the same format as the sample answer shown below.

31)

Find the radian measure of an angle whose measure is 135 degrees.

Click here to review the unit content explanation for Circular Trigonometry.

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In the following problems, use the function:

For responses that require non-keyboard symbols, the answers should be expressed in written form.

Example: Express p as pi.

Click here to review the unit content explanation for More Trigonometry.

32)

What is the amplitude?

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33)

What is the frequency?

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34)

What is the period?

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35) Extended Learning

Watch the following video, then write a five-sentence paragraph summarizing the video.

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