Question 1

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

The sequence is defined from $n = 1$ to $n = 15$, with a specific formula for each term. Since it has a clear end at $n = 15$, it is a finite sequence.

Question 2

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

The sequence is defined recursively with each term being 9 times the previous term, starting from a non-zero value. This process does not have a natural stopping point, making the sequence infinite.

Question 3

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

Accepted Answer

The sequence -5, -4, -3, -2 is finite because it has a clear beginning and end, with a limited number of terms.

Question 4

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

Accepted Answer

Substituting $n = 1, 2, 3, 4, 5$ into the formula $a_n = 2n - 1$ gives the first five terms as $1, 3, 5, 7, 9$.

Question 5

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

Accepted Answer

The sequence is defined by $\mathrm { a } _ { \mathrm { n } } = \mathrm { n } - 4$. Substituting $n = 1, 2, 3, 4, 5$ into the formula gives the first five terms as $-3, -2, -1, 0, 1$.

Question 6

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 $\mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } - 1 } ( 2 \mathrm { n } - 6 )$. For $n = 1$, $\mathrm { a } _ { 1 } = ( - 1 ) ^ { 0 } ( 2 \cdot 1 - 6 ) = 1 \cdot ( - 4 ) = - 4$.For $n = 2$, $\mathrm { a } _ { 2 } = ( - 1 ) ^ { 1 } ( 2 \cdot 2 - 6 ) = -1 \cdot ( - 2 ) = 2$.For $n = 3$, $\mathrm { a } _ { 3 } = ( - 1 ) ^ { 2 } ( 2 \cdot 3 - 6 ) = 1 \cdot 0 = 0$.For $n = 4$, $\mathrm { a } _ { 4 } = ( - 1 ) ^ { 3 } ( 2 \cdot 4 - 6 ) = -1 \cdot 2 = - 2$.For $n = 5$, $\mathrm { a } _ { 5 } = ( - 1 ) ^ { 4 } ( 2 \cdot 5 - 6 ) = 1 \cdot 4 = 4$.Thus, the first five terms are $- 4, 2, 0, - 2, 4$.

Question 7

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 $a _ { n } = \frac { n ^ { 2 } - 9 } { n ^ { 2 } + 9 }$. Calculating each term gives: - For $n = 1$, $a_1 = \frac{1^2 - 9}{1^2 + 9} = \frac{-8}{10} = -\frac{4}{5}$- For $n = 2$, $a_2 = \frac{2^2 - 9}{2^2 + 9} = \frac{4 - 9}{4 + 9} = \frac{-5}{13}$- For $n = 3$, $a_3 = \frac{3^2 - 9}{3^2 + 9} = \frac{0}{18} = 0$- For $n = 4$, $a_4 = \frac{4^2 - 9}{4^2 + 9} = \frac{7}{25}$- For $n = 5$, $a_5 = \frac{5^2 - 9}{5^2 + 9} = \frac{16}{34} = \frac{8}{17}$

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

The correct sequence is obtained by plugging in values of $n$ (starting from 1) into the formula $a_n = n^2 - n$. For $n=1$, $a_1 = 1^2 - 1 = 0$; for $n=2$, $a_2 = 2^2 - 2 = 2$; continuing this way gives the sequence $0, 2, 6, 12, 20$, which matches option B.

Question 10

Decide whether the given sequence is finite or infinite.&#10;-3, -2, -1, 0, . . .&#10;A) Infinite&#10;B) Finite

Accepted Answer

The sequence is infinite because it continues indefinitely, adding 1 each time, starting from -3 and moving towards positive infinity.

Question 11

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

Accepted Answer

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

Question 12

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

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

Question 17

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

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

Question 18

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Decide whether the given sequence is finite or infinite.&#10;

Accepted Answer

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

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

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

Accepted Answer

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

Question 24

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

Accepted Answer

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

Question 25

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

Accepted Answer

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

Question 26

Use a graphing calculator to evaluate the series.&#10;

Accepted Answer

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

Question 27

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

Accepted Answer

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

Question 28

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

Accepted Answer

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

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

Use a graphing calculator to evaluate the series.&#10;

Accepted Answer

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

Question 31

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

Accepted Answer

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

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;

Accepted Answer

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

Question 34

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

Accepted Answer

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

Question 35

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

Accepted Answer

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

Question 36

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

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;

Accepted Answer

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

Question 38

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

Accepted Answer

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

Question 39

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

Accepted Answer

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

Question 40

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

Accepted Answer

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

Question 41

Write the series using summation notation.&#10;

Accepted Answer

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

Question 42

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

Accepted Answer

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

Question 43

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

Question 44

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

Question 45

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 46

Write the series using summation notation.&#10;

Accepted Answer

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

Question 47

Write the series using summation notation.&#10;

Accepted Answer

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

Question 48

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

Question 49

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

Question 50

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 51

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

Question 52

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 53

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

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

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

Accepted Answer

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

Question 56

Evaluate the sum using the given information.&#10;x1 = 2, x2 = -3, x3 = -2, x4 = -5, and&#9651;x = -0.6; f(x) = x x- 5 4&#10;&#8721; f(xi)&#9651;x (Round to the nearest tenth, if necessary.)&#10;I=1&#10;A) 0.2&#10;B) -0.4&#10;C) 0&#10;D) -0.3

Accepted Answer

The answer of Evaluate the sum using the given information.&#10;x1...

Question 57

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

Question 58

Use the summation properties to evaluate the series. The following rules may be needed:  &#10;

Accepted Answer

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

Question 59

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

Accepted Answer

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

Question 60

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 61

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).&#10;

Accepted Answer

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

Question 62

Find a n and a 6 for the following arithmetic sequence.&#10;

Accepted Answer

The answer of Find a n and a 6 for...

Question 63

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 64

Find the common difference for the arithmetic sequence.&#10;

Accepted Answer

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

Deck 11: Further Topics in Algebra