Chapter Review
Chapter
Chapter 6
Section
Chapter Review
Solutions 49 Videos

Write the first three terms of each sequence, given the explicit formula for the nth term of the sequence.

f(n) = 3^{-n}

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Q1a

Write the first three terms of each sequence, given the explicit formula for the nth term of the sequence.

t_n = \dfrac{n+2}{n+1} + 1

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Q1b

Write the 16th term, given the explicit formula for the nth term of the sequence.

a) f(n) = n^2 - 6

b) t_n = \dfrac{n-2}{n}

Q2

Describe the pattern in each sequence. Write the next three terms of each sequence.

7, -14, 21, -28,...

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Q3a

Describe the pattern in each sequence. Write the next three terms of each sequence.

-\dfrac{1}{2}, \dfrac{1}{4}, -\dfrac{1}{8}, \dfrac{1}{16},...

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Q3b

Describe the pattern in each sequence. Write the next three terms of each sequence.

3x, 6x^2, 12x^3, 24x^4,...

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Q3c

For each sequence, create a table of values using the term number and term, and calculate the finite differences. Then, determine an explicit formula, in function notation, and specify the domain.

-5, -10, -15, -20, ...

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Q4a

For each sequence, create a table of values using the term number and term, and calculate the finite differences. Then, determine an explicit formula, in function notation, and specify the domain.

22, 23, 18, 7, ...

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Q4b

Write the first four terms of each sequence, where n e N.

f(1) = 2, f(n)=5n-f(n-1)

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Q5a

Write the first four terms of each sequence, where n e N.

f(1) = 5, f(n)=0.4f(n-1)

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Q5b

Write the first four terms of each sequence, where n e N.

f(1) = 10, f(n)=\dfrac{f(n-1)}{1-n}

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Q5c

Determine a recursion formula for each sequence.

1, 4, 13, 40, ...

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Q6a

Determine a recursion formula for each sequence.

3, 5, 7, 9, ...

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Q6b

Determine a recursion formula for each sequence.

-2, 2, -10, 26, ...

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Q6c

Write the first four terms of each sequence.

t_1 = \dfrac{1}{8}, t_n = 4t_{n-1}-1

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Q7a

Write the first four terms of each sequence.

f(1) = a - 2b, f(n) = f(n-1) + 3b

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Q7b

Anita convinces her dad to increase her allowance by 12% per week. In the first week she receives $5. a) Write a sequence to represent Anita’s allowance for 4 weeks. b) Write a recursion formula to represent her weekly allowance. c) Write an explicit formula for the nth term of the sequence. d) What will her allowance be after 10 weeks? e) After how many weeks will her allowance be$75.89?

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Q8

Use Pascal's triangle to list the numbers in a hockey stick pattern with each of the following sums.

210

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Q9a

Use Pascal's triangle to list the numbers in a hockey stick pattern with each of the following sums.

70

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Q9b

Use Pascal's triangle to list the numbers in a hockey stick pattern with each of the following sums.

126

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Q9c

Determine the sum of the terms in each of these rows of Pascal’s triangle.

row 21

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Q10a

Determine the sum of the terms in each of these rows of Pascal’s triangle.

row 18

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Q10b

Express as a single term from Pascal’s triangle in the form t_n, _r.

t_8, _6 + t_8, _7

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Q11a

Express as a single term from Pascal’s triangle in the form t_n, _r.

t_{12}, _2 + t_{12}, _3

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Q11b

Express as a single term from Pascal’s triangle in the form t_n, _r.

t_{23}, _{21} + t_{23}, _{22}

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Q11c

Use Pascal's triangle to expand each power of a binomial.

(a + 1)^5

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Q12a

Use Pascal's triangle to expand each power of a binomial.

(4x^2-3y^3)^4

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Q12b

Use Pascal's triangle to expand each power of a binomial.

(1-\dfrac{1}{x})^5

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Q12c

For each arithmetic sequence, determine the values of a and d and the formula for the general term. Then, write the next four terms.

-19, -25, -31, ...

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Q13a

For each arithmetic sequence, determine the values of a and d and the formula for the general term. Then, write the next four terms.

\dfrac{8}{3}, \dfrac{34}{15}, \dfrac{28}{15}, ...

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Q13b

Given the formula for the general term of an arithmetic sequence, determine t_{16}.

f(n) = 1 + \dfrac{1}{2}n

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Q14a

Given the formula for the general term of an arithmetic sequence, determine t_{16}.

t_n = 3.2n + 0.8

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Q14b

A jogger running along a path that goes up a hill runs a distance of 423 m in the first minute. As the hill becomes steeper, the jogger runs 14 m less in each subsequent minute.

a) Determine the general term for the sequence that represents this situation.

b) How far does the jogger run in the 12th minute?

c) In which minute does the jogger run 157 m?

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Q15

Determine whether the sequence is arithmetic, geometric, or neither. Give a reason for your answer.

\dfrac{3}{5}, \dfrac{5}{7}, \dfrac{7}{9}, \dfrac{9}{11}, ...

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Q16a

Determine whether the sequence is arithmetic, geometric, or neither. Give a reason for your answer.

2, 2 \sqrt 3, 6, 6 \sqrt 3

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Q16b

Determine whether the sequence is arithmetic, geometric, or neither. Give a reason for your answer.

x+7y, 2x+10y, 3x+13y,...

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Q16c

For each geometric sequence, determine the formula for the general term and use it to determine the specified term.

-3, 15, -75, ..., t_9

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Q17a

For each geometric sequence, determine the formula for the general term and use it to determine the specified term.

-\dfrac{2}{625}, \dfrac{2}{125}, -\dfrac{2}{25}, ..., t_{11}

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Q17b

A chain e-mail starts with three people each sending out five e-mail messages. Each of the recipients sends out five messages. and so on. How many e-mail messages will be sent in the ninth round of e-mailing?

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Q18

For each arithmetic series, state the values of a and d. Then, determine the sum of the first 10 terms.

21 + 15 + 9 + ...

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Q19a

For each arithmetic series, state the values of a and d. Then, determine the sum of the first 10 terms.

-4 - 9 - 14 - ...

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Q19b

Determine the sum of each arithmetic series.

52 + 47 + 42 + ... - 48

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Q20a

Determine the sum of each arithmetic series.

3 + 5.5 + 8 + ... + 133

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Q20b

A ball picks up speed as it rolls down a long steep hill. The ball travels 0.75 m in the first second, 1.25 m in the second, 1.75 m in the next second, and so on. Determine the total distance travelled by the ball in 40 s.

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Q21

Determine an arithmetic series such that the sum of the first 9 terms of the series is 162 and the sum of the first 12 terms is 288.

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Q22

For the geometric series 100 - 200 + 400 - ..., determine the values of a and r. Then, determine S_8.

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Q23

Determine the sum of each geometric series.

2 + 6 + 18 + ... + 1458

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Q24a

Determine the sum of each geometric series.

1 - \dfrac{1}{3} + \dfrac{1}{9} - ... - \dfrac{1}{19 683}

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Q24b

The sum of the first two terms of a geometric series is 12 and the sum of the first three terms is 62. Determine the series.