Question 1

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

Accepted Answer

The sequence $\left\{ 2 ^ { n } \right\}$ represents an exponential sequence where each term is 2 raised to the power of n, starting with n=1. The first five terms are $2^1=2$, $2^2=4$, $2^3=8$, $2^4=16$, and $2^5=32$, which matches option A.

Question 2

Evaluate the factorial expression.&#10;

Accepted Answer

The expression simplifies to $\frac{n}{n+10}$ by canceling out the common $(n+9)!$ in the numerator and denominator.

Question 3

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

Accepted Answer

To find the first five terms of the sequence $\{ 4n - 2 \}$, substitute $n = 1, 2, 3, 4, 5$ into the formula. For $n=1$, the term is $4(1)-2=2$; for $n=2$, it's $4(2)-2=6$; continuing this way gives the sequence $2, 6, 10, 14, 18$.

Question 4

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

Accepted Answer

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

Question 5

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.&#10;

Accepted Answer

The sequence increases by 3 each time (common difference in an arithmetic sequence). The first term is 1, so the nth term is given by $a_n = 1 + (n-1) \times 3 = 3n - 2$.

Question 6

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

Accepted Answer

The sequence is defined by the formula $n^2 - n$, where $n$ starts from 1. Plugging in the values 1, 2, 3, 4, and 5 into the formula gives the sequence 0, 2, 6, 12, 20.

Question 7

Write the first four terms of the sequence whose general term is given.&#10;

Accepted Answer

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

Question 8

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

Accepted Answer

The sequence is given by $(-1)^{n-1} \left(\frac{n+1}{2n-1}\right)$. For $n=1$, the term is $2$; for $n=2$, the term is $-1$; for $n=3$, the term is $\frac{4}{5}$; for $n=4$, the term is $-\frac{5}{7}$; and for $n=5$, the term is $\frac{2}{3}$.

Question 9

Evaluate the factorial expression.&#10;

Accepted Answer

The factorial of a number $n!$ is the product of all positive integers less than or equal to $n$. Thus, $2! = 2 \times 1 = 2$ and $4! = 4 \times 3 \times 2 \times 1 = 24$. Therefore, $\frac{2!}{4!} = \frac{2}{24} = \frac{1}{12}$.

Question 10

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

Accepted Answer

The sequence is defined by the formula $4(4n - 2)$. Substituting $n = 1, 2, 3, 4, 5$ into the formula gives the first five terms as $8, 24, 40, 56, 72$.

Question 11

Evaluate the factorial expression.&#10;

Accepted Answer

The answer of Evaluate the factorial expression.&#10; ...

Question 12

Evaluate the factorial expression.&#10;

Accepted Answer

The answer of Evaluate the factorial expression.&#10; ...

Question 13

Write the first four terms of the sequence whose general term is given.&#10;

Accepted Answer

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

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

Evaluate the factorial expression.&#10;

Accepted Answer

The answer of Evaluate the factorial expression.&#10; ...

Question 16

Evaluate the factorial expression.&#10;

Accepted Answer

The answer of Evaluate the factorial expression.&#10; ...

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

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.&#10;

Accepted Answer

The answer of The given pattern continues. Write down the...

Question 19

Evaluate the factorial expression.&#10;

Accepted Answer

The answer of Evaluate the factorial expression.&#10; ...

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

Write out the sum. Do not evaluate.&#10;

Accepted Answer

The answer of Write out the sum. Do not evaluate.&#10;...

Question 22

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 23

Write out the sum. Do not evaluate.&#10;

Accepted Answer

The answer of Write out the sum. Do not evaluate.&#10;...

Question 24

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 25

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 26

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.&#10;

Accepted Answer

The answer of The given pattern continues. Write down the...

Question 27

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.&#10;

Accepted Answer

The answer of The given pattern continues. Write down the...

Question 28

Write out the sum. Do not evaluate.&#10;

Accepted Answer

The answer of Write out the sum. Do not evaluate.&#10;...

Question 29

Write out the sum. Do not evaluate.&#10;

Accepted Answer

The answer of Write out the sum. Do not evaluate.&#10;...

Question 30

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 31

Write out the sum. Do not evaluate.&#10;

Accepted Answer

The answer of Write out the sum. Do not evaluate.&#10;...

Question 32

The sequence is defined recursively. Write the first four terms.&#10;

Accepted Answer

The answer of The sequence is defined recursively. Write the...

Question 33

Write the word or phrase that best completes each statement or answers the question.&#10;

Accepted Answer

The answer of Write the word or phrase that best...

Question 34

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.&#10;

Accepted Answer

The answer of The given pattern continues. Write down the...

Question 35

Choose the one alternative that best completes the statement or answers the question.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 36

Choose the one alternative that best completes the statement or answers the question.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 37

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 38

The sequence is defined recursively. Write the first four terms.&#10;

Accepted Answer

The answer of The sequence is defined recursively. Write the...

Question 39

The sequence is defined recursively. Write the first four terms.&#10;

Accepted Answer

The answer of The sequence is defined recursively. Write the...

Question 40

The sequence is defined recursively. Write the first four terms.&#10;

Accepted Answer

The answer of The sequence is defined recursively. Write the...

Question 41

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 42

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of&#10;summation.&#10;

Accepted Answer

The answer of Express the sum using summation notation with...

Question 43

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of&#10;summation.&#10;

Accepted Answer

The answer of Express the sum using summation notation with...

Question 44

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 45

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 46

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 47

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 48

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 49

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 50

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 51

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of&#10;summation.&#10;

Accepted Answer

The answer of Express the sum using summation notation with...

Question 52

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of&#10;summation.&#10;

Accepted Answer

The answer of Express the sum using summation notation with...

Question 53

Express the sum using summation notation.&#10;

Accepted Answer

The answer of Express the sum using summation notation.&#10; ...

Question 54

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 55

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 56

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 57

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 58

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 59

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 60

Find the sum of the sequence.&#10;

Accepted Answer

The answer of Find the sum of the sequence.&#10; ...

Question 61

Solve.&#10;

Accepted Answer

The answer of Solve.&#10; ...

Question 62

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are&#10;given.&#10;

Accepted Answer

The answer of Find the nth term and the indicated...

Question 63

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are&#10;given.&#10;

Accepted Answer

The answer of Find the nth term and the indicated...

Question 64

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are&#10;given.&#10;

Accepted Answer

The answer of Find the nth term and the indicated...

Deck 11: Sequences; Induction; the Binomial Theorem