Discrete Functions Chapter Review
Chapter
Chapter 6
Section
Discrete Functions Chapter Review
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Solutions 35 Videos

Given the explicit formula, determine the first four terms in each sequence

  • t_n = 4+ 2n^2, n \in \mathbb{N}
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0.44mins
Q1a

Given the explicit formula, determine the first four terms in each sequence.

  • f(n) = \frac{2n -1}{n}, n \in \mathbb{N}
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0.34mins
Q1b

For the sequence, make a table of values using the term number and term. Then, graph the sequence using the ordered pairs (term number, term) and determine an explicit formula for the nth term, using function notation.

-8, -11, -14, -17, ...

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0.41mins
Q2a

For the sequence, make a table of values using the term number and term. Then, graph the sequence using the ordered pairs (term number, term) and determine an explicit formula for the nth term, using function notation.

3, 2, -3, -12, ...

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4.34mins
Q2b

Write the first four terms of each sequence, where n \in \mathbb{N}.

f(1) = 5, f(n) = f(n-1) - 4

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0.32mins
Q3a

Write the first four terms of each sequence, where n \in \mathbb{N}.

t_1=3, t_n = 2t_{n - 1} - n

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0.45mins
Q3b

Determine a recursion formula for each sequence.

-2, 7, 16, 25 ,...

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0.23mins
Q4a

Determine a recursion formula for each sequence.

1, -3, 9, -27, ...

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0.20mins
Q4b

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

(x + 4)^5

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0.40mins
Q5a

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

(y - 6)^4

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0.39mins
Q5b

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

(m + 2n)^4

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0.53mins
Q5c

Use Pascal's triangle to expand each power of a binomial. (3p- q)^6

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0.59mins
Q5d

Recall that the sequence of triangular numbers 1, 3, 6, 10, 15, can be found in Pascal's triangle. Tetrahedral numbers are the sums of consecutive triangular numbers 1, 4, 10, 20,...

  • Write the next two terms of the sequence representing tetrahedral numbers.
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1.41mins
Q6a

Recall that the sequence of triangular numbers 1, 3, 6, 10, 15, can be found in Pascal's triangle. Tetrahedral numbers are the sums of consecutive triangular numbers 1, 4, 10, 20,...

  • Locate these numbers in Pascal's triangle. Describe their position.
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0.16mins
Q6b

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

3, 1, -1 -3, ...

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0.37mins
Q7a

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

\displaystyle \frac{2}{3}, \frac{11}{12}, \frac{7}{6}, \frac{17}{12}, ...

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1.18mins
Q7b

Given the formula for the general term of an arithmetic sequence, write the first three terms. Graph the discrete function that represents each sequence.

f(n) =4n - 3

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1.12mins
Q8a

Given the formula for the general term of an arithmetic sequence, write the first three terms. Graph the discrete function that represents each sequence.

f(n) =5 - 4n

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1.22mins
Q8b

A theatre has 40 rows of seats. Each row has five more seats than the previous row. If the first row has 50 seats, how many seats are in the

(a) 20th row?

(b) last row?

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0.57mins
Q9

Determine whether the sequence is arithmetic, geometric, or neither. Justify your answers.

  • -1, 9, 19, 29, ...
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0.19mins
Q10a

Determine whether the sequence is arithmetic, geometric, or neither. Justify your answers.

  • 3, 12, 19, 44, ...
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0.25mins
Q10b

Determine whether the sequence is arithmetic, geometric, or neither. Justify your answers.

  • -2, 6, -18, 54, ...
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0.28mins
Q10c

Write the first three terms of each geometric sequence.

f(n) = 2(-1)^n

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0.21mins
Q11a

Write the first three terms of each geometric sequence.

t_n = -3(2)^{n+ 1}

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0.42mins
Q11b

Angelica ran in a half marathon. The length of the race was 21.1 km. She ran 1700 m in the first 10 min of the race. In each 10-min interval after the first one, her distance decreased by 4%. How far did she run in the tenth 10-min interval?

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1.21mins
Q12

For each arithmetic series, state the values of a and d. Then. determine the sum of the first 20 terms.

  • 50 + 45 + 40 + ...
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0.48mins
Q13a

For each arithmetic series, state the values of a and d. Then. determine the sum of the first 20 terms.

-27 - 21,-15 - ...

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0.57mins
Q13b

On his 12th birthday, Eric's grandparents deposited $25 into a savings account for him. Each month after that up to and including his 20th birthday, they deposit $10 more than the previous month. How much money will Enoch have on his 20th birthday, excluding interest?

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2.44mins
Q14

Determine the sum of the arithmetic series.

-6 -13 -20 - ... - 139

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1.18mins
Q15a

Determine the sum of the arithmetic series.

-23 -17 -11 - ... + 43

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1.19mins
Q15b

For the geometric series, determine the values of a and r. Then, determine the sum of the first 10 terms.

  • 2 + 14 + 98 + ...
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0.35mins
Q16a

For the geometric series, determine the values of a and r. Then, determine the sum of the first 10 terms.

  • 8 - 16 + 32 - 64 + ...
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0.42mins
Q16b

Determine the sum of the geometric series.

245 +24.5 + 2.45 + ... + 0.000 245

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1.23mins
Q17a

Determine the sum of the geometric series.

6561 + 2187 + 729 + ... + \frac{1}{6561}

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2.20mins
Q17b

The first four diagrams in a pattern are shown. Each shape is made of small squares with an area of 0.5 cm^2. Determine the total area of the first 10 diagrams.

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1.13mins
Q18