Question 1

Decide whether the given sequence is finite or infinite.&#10; &#10;A) Infinite&#10;B) Finite

Accepted Answer

The sequence is defined for $n$ from 1 to 10, with a specific formula for $n$ from 3 to 10. This means it has a clear end at $n = 10$, making it finite.

Question 2

Write out the first five terms of the sequence.&#10;

Accepted Answer

The sequence is defined by $a_n = \frac{3}{n^2}$, so for the first five terms, we substitute $n$ with 1, 2, 3, 4, and 5 respectively, resulting in $3, \frac{3}{4}, \frac{1}{3}, \frac{3}{16}, \frac{3}{25}$.

Question 3

Decide whether the given sequence is finite or infinite.&#10; &#10;A) Infinite&#10;B) Finite

Accepted Answer

The sequence is defined recursively with each term being generated from the previous one without a specified endpoint, making it infinite.

Question 4

Write out the first five terms of the sequence.&#10;

Accepted Answer

To find the first five terms of the sequence, substitute $n = 1, 2, 3, 4, 5$ into the formula $a _ { n } = \frac { n ^ { 2 } - 6 } { n ^ { 2 } + 6 }$ and simplify:- For $n = 1$, $a_1 = \frac{1^2 - 6}{1^2 + 6} = \frac{-5}{7}$- For $n = 2$, $a_2 = \frac{2^2 - 6}{2^2 + 6} = \frac{-2}{10} = -\frac{1}{5}$- For $n = 3$, $a_3 = \frac{3^2 - 6}{3^2 + 6} = \frac{3}{15} = \frac{1}{5}$- For $n = 4$, $a_4 = \frac{4^2 - 6}{4^2 + 6} = \frac{10}{22} = \frac{5}{11}$- For $n = 5$, $a_5 = \frac{5^2 - 6}{5^2 + 6} = \frac{19}{31}$

Question 5

Write out the first five terms of the sequence.&#10;

Accepted Answer

The sequence is generated by substituting $n$ with 1, 2, 3, 4, and 5 into the formula $a_n = 2(2n - 3)$. This results in the terms -2, 2, 6, 10, and 14 respectively.

Question 6

Decide whether the given sequence is finite or infinite.&#10; &#10;A) Finite&#10;B) Infinite

Accepted Answer

The sequence is defined from $n = 1$ to $n = 40$, which means it has a clear beginning and end. Therefore, it is finite.

Question 7

Find the first six terms of the sequence.&#10;

Accepted Answer

The given sequence starts with $a_1 = 5$ and each subsequent term is obtained by adding 7 to the previous term. Thus, the first six terms are $5, 12, 19, 26, 33, 40$.

Question 8

Decide whether the given sequence is finite or infinite.&#10; &#10;A) Finite&#10;B) Infinite

Accepted Answer

The sequence is defined recursively with each term being generated from the previous two terms. There is no specified endpoint for the sequence, so it continues indefinitely as long as the recursive formula is applied.

Question 9

Decide whether the given sequence is finite or infinite.&#10;-1, 0, 1, 2, . . .&#10;A) Infinite&#10;B) Finite

Accepted Answer

The sequence starts at -1 and increases by 1 each time without a specified end, making it infinite.

Question 10

Write out the first five terms of the sequence.&#10;

Accepted Answer

Substituting $n = 1, 2, 3, 4, 5$ into the formula $a_n = \frac{2n - 1}{n^2 + 2n}$ gives the sequence $\frac{1}{3}, \frac{3}{8}, \frac{1}{3}, \frac{7}{24}, \frac{9}{35}$, matching option B.

Question 11

Decide whether the given sequence is finite or infinite.&#10;-5, -4, -3, -2&#10;A) Finite&#10;B) Infinite

Accepted Answer

The answer of Decide whether the given sequence is finite...

Question 12

Decide whether the given sequence is finite or infinite.&#10;6, 7, 8, 9&#10;A) Infinite&#10;B) Finite

Accepted Answer

The answer of Decide whether the given sequence is finite...

Question 13

Decide whether the given sequence is finite or infinite.&#10; &#10;A) Finite&#10;B) Infinite

Accepted Answer

The answer of Decide whether the given sequence is finite...

Question 14

Write out the first five terms of the sequence.&#10;

Accepted Answer

The answer of Write out the first five terms of...

Question 15

Write out the first five terms of the sequence.&#10;

Accepted Answer

The answer of Write out the first five terms of...

Question 16

Write out the first five terms of the sequence.&#10;

Accepted Answer

The answer of Write out the first five terms of...

Question 17

Write out the first five terms of the sequence.&#10;

Accepted Answer

The answer of Write out the first five terms of...

Question 18

Decide whether the given sequence is finite or infinite.&#10;9, 10, 11, 12, . . .&#10;A) Infinite&#10;B) Finite

Accepted Answer

The answer of Decide whether the given sequence is finite...

Question 19

Decide whether the given sequence is finite or infinite.&#10; &#10;A) Infinite&#10;B) Finite

Accepted Answer

The answer of Decide whether the given sequence is finite...

Question 20

Write out the first five terms of the sequence.&#10;

Accepted Answer

The answer of Write out the first five terms of...

Question 21

Evaluate the sum. Round to two decimal places, if necessary.&#10;

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 22

Find the first six terms of the sequence.&#10;

Accepted Answer

The answer of Find the first six terms of the...

Question 23

Evaluate the sum using the given information.&#10;

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 24

Evaluate the sum. Round to two decimal places, if necessary.&#10; &#10;A) -26&#10;B) 2&#10;C) 26&#10;D) 18

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 25

Evaluate the sum using the given information.&#10; &#10;A) -26&#10;B) -23&#10;C) -34&#10;D) 18

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 26

Find the first six terms of the sequence.&#10;

Accepted Answer

The answer of Find the first six terms of the...

Question 27

Evaluate the sum. Round to two decimal places, if necessary.&#10; &#10;A) -6&#10;B) -30&#10;C) 81&#10;D) 30

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 28

Evaluate the sum. Round to two decimal places, if necessary.&#10; &#10;A) 42&#10;B) 38&#10;C) 33&#10;D) 23

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 29

Evaluate the sum. Round to two decimal places, if necessary.&#10;

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 30

Find the first six terms of the sequence.&#10;

Accepted Answer

The answer of Find the first six terms of the...

Question 31

Use a graphing calculator to evaluate the series.&#10; &#10;A) 1010&#10;B) 110&#10;C) 1164&#10;D) 264

Accepted Answer

The answer of Use a graphing calculator to evaluate the...

Question 32

Evaluate the sum. Round to two decimal places, if necessary.&#10;

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 33

Evaluate the sum. Round to two decimal places, if necessary.&#10; &#10;A) 26&#10;B) 174&#10;C) -174&#10;D) 30,558

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 34

Evaluate the sum using the given information.&#10; &#10;A) -7&#10;B) 5&#10;C) -15&#10;D) -13

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 35

Evaluate the sum. Round to two decimal places, if necessary.&#10;

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 36

Evaluate the sum. Round to two decimal places, if necessary.&#10; &#10;A) 0.75&#10;B) 38&#10;C) 0.43&#10;D) -0.7

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 37

Evaluate the sum. Round to two decimal places, if necessary.&#10; &#10;A) -4.69&#10;B) 1.42&#10;C) -6.42&#10;D) 172.5

Accepted Answer

The answer of Evaluate the sum. Round to two decimal...

Question 38

Find the first six terms of the sequence.&#10;

Accepted Answer

The answer of Find the first six terms of the...

Question 39

Evaluate the sum using the given information.&#10; &#10;A) 32&#10;B) 45&#10;C) 24&#10;D) 31

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 40

Use a graphing calculator to evaluate the series.&#10; &#10;A) 116.67&#10;B) 322&#10;C) 490&#10;D) -28

Accepted Answer

The answer of Use a graphing calculator to evaluate the...

Question 41

Write the series using summation notation.&#10;

Accepted Answer

The answer of Write the series using summation notation.&#10; ...

Question 42

Write the series using summation notation.&#10;

Accepted Answer

The answer of Write the series using summation notation.&#10; ...

Question 43

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or&#10;diverges.&#10; &#10;A) Diverges&#10;B) Converges

Accepted Answer

The answer of Graph the function corresponding to the sequence...

Question 44

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or&#10;diverges.&#10; &#10;A) Converges&#10;B) Diverges

Accepted Answer

The answer of Graph the function corresponding to the sequence...

Question 45

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) 462&#10;B) 112&#10;C) 441&#10;D) 1764

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 46

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) - 23&#10;B) - 3&#10;C) 23&#10;D) - 33

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 47

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) 80&#10;B) 120&#10;C) 100&#10;D) 40

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 48

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) 57&#10;B) 39&#10;C) 63&#10;D) 51

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 49

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or&#10;diverges.&#10; &#10;A) Diverges&#10;B) Converges

Accepted Answer

The answer of Graph the function corresponding to the sequence...

Question 50

Evaluate the sum using the given information.&#10; &#10;A) 75.6&#10;B) 18.9&#10;C) 16.4934&#10;D) 19.9

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 51

Evaluate the sum using the given information.&#10; &#10;A) 5.193&#10;B) -148.8&#10;C) -37.2&#10;D) -36.2

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 52

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or&#10;diverges.&#10; &#10;A) Converges&#10;B) Diverges

Accepted Answer

The answer of Graph the function corresponding to the sequence...

Question 53

Evaluate the sum using the given information.&#10;

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 54

Evaluate the sum using the given information.&#10;

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 55

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) 417&#10;B) 108&#10;C) 88&#10;D) 437

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 56

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) - 150&#10;B) - 84&#10;C) - 216&#10;D) 132

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 57

Write the series using summation notation.&#10;

Accepted Answer

The answer of Write the series using summation notation.&#10; ...

Question 58

Evaluate the sum using the given information.&#10; &#10;A) -1&#10;B) -2.4&#10;C) -2.2&#10;D) 3.4

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;...

Question 59

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) - 5340&#10;B) - 445&#10;C) - 1780&#10;D) 5

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 60

Use the summation properties to evaluate the series. The following rules may be needed:  &#10; &#10;A) 84&#10;B) 42&#10;C) 21&#10;D) 300

Accepted Answer

The answer of Use the summation properties to evaluate the...

Question 61

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).&#10;The first term is 21, and the common difference is 7; n = 5&#10;A) 21, 7, 56, 84, 112&#10;B) 21, 28, 35, 42, 49&#10;C) 7, 28, 49, 70, 91&#10;D) 21, 7, 35, 42, 49

Accepted Answer

The answer of Write the first n terms of the...

Question 62

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or&#10;diverges.&#10;

Accepted Answer

The answer of Graph the function corresponding to the sequence...

Question 63

Find the common difference for the arithmetic sequence.&#10;4, 5, 6, 7, . .&#10;A) -1&#10;B) 3&#10;C) 0.01&#10;D) 1

Accepted Answer

The answer of Find the common difference for the arithmetic...

Question 64

Find the common difference for the arithmetic sequence.&#10;-7, -11, -15, -19, . . .&#10;A) -8&#10;B) -12&#10;C) -4&#10;D) -8.6

Accepted Answer

The answer of Find the common difference for the arithmetic...

Deck 12: Further Topics in Algebra