Chapter Sequences and Series Review
Chapter
Chapter 7
Section
Chapter Sequences and Series Review
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Solutions 65 Videos

Represent the sequence 2, 8, 14, 20, ... in words

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0.44mins
Q1a

Represent the sequence 2, 8, 14, 20, ... algebraically

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0.23mins
Q1b

Represent the sequence 2, 8, 14, 20, ... graphically

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0.51mins
Q1c

How can you determine whether a sequence is arithmetic?

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0.26mins
Q2

For each arithmetic sequence, state

  • i) the general term
  • ii) the recursive formula

58, 73, 88, ...

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0.59mins
Q3a

For each arithmetic sequence, state

  • i) the general term
  • ii) the recursive formula

-49, -40, -31, ...

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1.01mins
Q3b

Determine the 100th term of the arithmetic sequence with t_7 = 465 and t_{13} = 219.

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1.36mins
Q4

A student planets a seed. After the seed sprouts, the student monitors the growth of the plant by measuring its height every week. The height after each of the first three weeks was 7 m, 20 mm and 33 mm, respectively. If this pattern of growth continues, in what week will the plant be more than 100 mm tall?

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1.20mins
Q5

How can you determine whether a sequence is geometric?

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0.35mins
Q6
  • i) Determine whether each sequence is arithmetic, geometric, or neither.
  • ii) Determine whether each sequence is arithmetic, geometric, or neither.

5, 15, 45, ...

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0.38mins
Q7a
  • i) Determine whether each sequence is arithmetic, geometric, or neither.
  • ii) Determine whether each sequence is arithmetic, geometric, or neither.

0, 3, 8, ...

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0.14mins
Q7b
  • i) Determine whether each sequence is arithmetic, geometric, or neither.
  • ii) Determine whether each sequence is arithmetic, geometric, or neither.

288, 14.4, 0.72, ...

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0.55mins
Q7c
  • i) Determine whether each sequence is arithmetic, geometric, or neither.
  • ii) Determine whether each sequence is arithmetic, geometric, or neither.

410, 50, 90, ...$

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0.35mins
Q7d
  • i) Determine whether each sequence is arithmetic, geometric, or neither.
  • ii) Determine whether each sequence is arithmetic, geometric, or neither.

19, 10, 1, ...

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0.22mins
Q7e
  • i) Determine whether each sequence is arithmetic, geometric, or neither.
  • ii) Determine whether each sequence is arithmetic, geometric, or neither.

512, 384, 288, ...

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0.48mins
Q7f

For each geometric sequence, determine

  • i) the recursive formula
  • ii) the general term
  • iii) the first five terms

The first term is 7 and the common riot is -3

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0.50mins
Q8a

For each geometric sequence, determine

  • i) the recursive formula
  • ii) the general term
  • iii) the first five terms

a =12 and r = \frac{1}{2}

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0.43mins
Q8b

For each geometric sequence, determine

  • i) the recursive formula
  • ii) the general term
  • iii) the first five terms

the second term is 36 and the third term is 144

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1.28mins
Q8c
  • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}.
  • ii) State the first five terms.

t_n = 4n + 5

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0.46mins
Q9a
  • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}.
  • ii) State the first five terms.

t_n = \frac{1}{7n -3}

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0.58mins
Q9b
  • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}.
  • ii) State the first five terms.

t_n = n^2 -1

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0.41mins
Q9c
  • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}.
  • ii) State the first five terms.

t_1 = -17, t_n =t_{n - 1} + n - 1, where n >1

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1.03mins
Q9d

In a laboratory experiment, the count of a certain bacteria doubles every hour.

a) At 1pm, there were 23000 bacteria present. How many bacteria will be present at midnight?

b) Can this model be sued to determine the bacterial population at any time? Explain.

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1.30mins
Q10

Guy purchased a rare stamp for \$820 in 2001. If the value of the stamp increases by 10\% per year, how much will the stamp be worth in 2010?

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0.57mins
Q11

Toothpicks are used to make a sequence of stacked squares as shown. Determine a rule for calculating t_n, the number of toothpicks needed for a stack of squares n high. Explain your reasoning.

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4.01mins
Q12

Determine the 100th term of the sequence

\displaystyle \frac{1}{2}, \frac{2}{5}, \frac{3}{8}, \frac{4}{11}, ...

Explain your reasoning.

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1.00mins
Q13

For each arithmetic series, calculate the sum of the first 50 terms.

\displaystyle 1 + 9 + 17 + ...

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0.51mins
Q14a

For each arithmetic series, calculate the sum of the first 50 terms.

\displaystyle 21 + 17 + 13 + ...

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1.02mins
Q14b

For each arithmetic series, calculate the sum of the first 50 terms.

\displaystyle 31 + 52 + 73 + ...

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0.57mins
Q14c

For each arithmetic series, calculate the sum of the first 50 terms.

\displaystyle -9 - 14 - 19 - ...

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0.29mins
Q14d

For each arithmetic series, calculate the sum of the first 50 terms.

\displaystyle 17.5 + 18.9 + 20.3 + ...

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0.36mins
Q14e

For each arithmetic series, calculate the sum of the first 50 terms.

\displaystyle 39 -31 - 23 ...

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0.36mins
Q14f

Determine the sum of the first 25 terms of an arithmetic series in which

the first term is 24 and the common difference is 11

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0.30mins
Q15a

Determine the sum of the first 25 terms of an arithmetic series in which

t_1 =91 and t_{25} = 374

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1.09mins
Q15b

Determine the sum of the first 25 terms of an arithmetic series in which

t_1 = 84 and t_2 = 57

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0.45mins
Q15c

Determine the sum of the first 25 terms of an arithmetic series in which

the third term is 42 and the terms decrease by 11

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1.12mins
Q15d

Determine the sum of the first 25 terms of an arithmetic series in which

the 12th term is 19 and the terms decrease by 4

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0.58mins
Q15e

Determine the sum of the first 25 terms of an arithmetic series in which

t_5 = 142 and t_{15} = 12

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1.17mins
Q15f

Calculate the sum of each series.

1 + 13 + 25 + ... + 145

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1.05mins
Q16a

Calculate the sum of each series.

9 + 42+75 + ...+ 4068

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1.42mins
Q16b

Calculate the sum of each series.

123 + 118 + 113 + ... - 122

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1.20mins
Q16c

A spacecraft leaves an orbiting space station to descend to the planet below. The spacecraft descends 64 m during the first second and then engages its reverse thrusters to slow down its descent. It travels 7 m less during each second afterward. If the spacecraft lands after 10 s, how far did it descent?

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1.23mins
Q17

For each geometric series, calculate t_6 and S_6.

\displaystyle 11 + 33 + 99 + ...

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0.34mins
Q18a

For each geometric series, calculate t_6 and S_6.

\displaystyle 0.111 111 + 1. 111 111 + 11. 111111 + ...

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1.29mins
Q18b

For each geometric series, calculate t_6 and S_6.

\displaystyle 6 - 12 + 24 - ...

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0.57mins
Q18c

For each geometric series, calculate t_6 and S_6.

\displaystyle 11 + 33 + 99 + ...

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1.23mins
Q18d

For each geometric series, calculate t_6 and S_6.

\displaystyle 17 - 25.5 + 38.25 - ...

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1.24mins
Q18e

For each geometric series, calculate t_6 and S_6.

\displaystyle \frac{1}{2} + \frac{3}{10} + \frac{9}{50} + ...

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1.28mins
Q18f

Determine the sum of the first eight terms of the geometric series in which

the first term is -6 and the common ratio is 4

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0.22mins
Q19a

Determine the sum of the first eight terms of the geometric series in which

t_1 = 42 and t_9 = 2112

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1.27mins
Q19b

Determine the sum of the first eight terms of the geometric series in which

the first term is 320 and the second terms is 80

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1.06mins
Q19c

Determine the sum of the first eight terms of the geometric series in which

the third term is 35 and the terms increase by a factor of 5

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1.05mins
Q19d

A catering company has 15 customer orders during its first month. for each month afterward, the company has double the number of orders than the previous month . How many orders in total did the company fill at the end of its first year?

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0.41mins
Q20

The 1st, 5th, and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometrid sequence.

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2.58mins
Q21

Calculate the sum of each series.

\displaystyle 7 + 14 + 28 + ... + 3584

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1.08mins
Q22a

Calculate the sum of each series.

\displaystyle -3 -6 -12 -24 - ... - 768

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1.32mins
Q22b

Calculate the sum of each series.

\displaystyle 1 + \frac{5}{2} + \frac{25}{4} + ... + \frac{15625}{64}

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1.04mins
Q22c

Calculate the sum of each series.

\displaystyle 96 000 - 48000 + 24 000 - ... + 375

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2.12mins
Q22d

Calculate the sum of each series.

\displaystyle 1000 + 1000(1.06) +1000(1.06)^2 + ... + 1000(1.06)^{12}

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0.50mins
Q22e

Expand and simplify.

(a + 6)^4

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1.00mins
Q23a

Expand and simplify.

(b-3)^5

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0.53mins
Q23b

Expand and simplify.

(2c+ 5)^3

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1.04mins
Q23c

Expand and simplify.

\displaystyle (4 - 3d)^6

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1.46mins
Q23d

Expand and simplify.

\displaystyle (3f^2-\frac{2}{f})^4

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1.35mins
Q23e

Expand and simplify.

(3f^2 - \frac{2}{f})^4

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1.52mins
Q23f