Question 1

Find the indicated term for the sequence whose general term is given.&#10;

Accepted Answer

To find the fifth term ($a_5$) in the sequence, substitute $n = 5$ into the formula $a_n = 4n - 1$. This gives $a_5 = 4(5) - 1 = 20 - 1 = 19$.

Question 2

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

Accepted Answer

The first five terms are found by substituting $n = 1, 2, 3, 4, 5$ into the formula $a_n = n^2 - n$, resulting in $0, 2, 6, 12, 20$.

Question 3

Find the indicated term for the sequence whose general term is given.&#10;

Accepted Answer

The general term is $a_n = \frac{(-1)^n}{n+8}$. For $a_{19}$, substitute $n = 19$: $a_{19} = \frac{(-1)^{19}}{19+8} = \frac{-1}{27} = -\frac{1}{27}$.

Question 4

Find a general term an for the sequence whose first four terms are given.&#10;

Accepted Answer

The sequence is geometric with a common ratio of 2. The general term for a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, where $a_1 = 2$ and $r = 2$. Thus, $a_n = 2 \cdot 2^{n-1} = 2^n$.

Question 5

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

Accepted Answer

The sequence is generated by substituting values of $n$ (starting from 1) into the formula $a_n = (-1)^n(n + 3)$. For the first five terms, when $n = 1, 2, 3, 4, 5$, the terms are $-4, 5, -6, 7, -8$ respectively, following the pattern of alternating signs due to the $(-1)^n$ factor.

Question 6

Find a general term an for the sequence whose first four terms are given.&#10;

Accepted Answer

The answer of Find a general term an for the...

Question 7

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

Accepted Answer

The general term of the sequence is $a_n = 4n$. To find the first five terms, substitute $n = 1, 2, 3, 4, 5$ into the formula. This gives $4(1) = 4$, $4(2) = 8$, $4(3) = 12$, $4(4) = 16$, and $4(5) = 20$, which matches option B.

Question 8

Find a general term an for the sequence whose first four terms are given.&#10;

Accepted Answer

The given sequence is $\frac{1}{1^2}, \frac{1}{2^2}, \frac{1}{3^2}, \frac{1}{4^2}, \ldots$, which follows the pattern $a_n = \frac{1}{n^2}$.

Question 9

Find the indicated term for the sequence whose general term is given.&#10;

Accepted Answer

To find $a_7$, substitute $n = 7$ into the general term formula: $a_n = 4 - n^2$. Thus, $a_7 = 4 - 7^2 = 4 - 49 = -45$.

Question 10

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

Accepted Answer

The sequence defined by $a_n = 2^n$ starts with $n=1$, so the first five terms are $2^1=2$, $2^2=4$, $2^3=8$, $2^4=16$, and $2^5=32$.

Question 11

Find a general term an for the sequence whose first four terms are given.&#10;

Accepted Answer

The answer of Find a general term an for the...

Question 12

Find the indicated term for the sequence whose general term is given.&#10;

Accepted Answer

The answer of Find the indicated term for the sequence...

Question 13

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

Accepted Answer

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

Question 14

Find the indicated term for the sequence whose general term is given.&#10;

Accepted Answer

The answer of Find the indicated term for the sequence...

Question 15

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

Accepted Answer

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

Question 16

Find the indicated term for the sequence whose general term is given.&#10;

Accepted Answer

The answer of Find the indicated term for the sequence...

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Find the indicated term for the sequence whose general term is given.&#10;

Accepted Answer

The answer of Find the indicated term for the sequence...

Question 21

Solve the problem.&#10;

Accepted Answer

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

Question 22

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 23

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given.&#10;

Accepted Answer

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

Question 24

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 25

Solve the problem.&#10;

Accepted Answer

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

Question 26

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 27

Solve the problem.&#10;

Accepted Answer

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

Question 28

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given.&#10;

Accepted Answer

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

Question 29

Solve the problem.&#10;

Accepted Answer

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

Question 30

Solve the problem.&#10;Doctors predict that by administering a vaccine, the number of new cases of a certain childhood disease will decrease by half each year. If 1000 people were afflicted with the disease in 2010,&#10;Estimate the number of new cases in 2015. (Round to the nearest whole number, if necessary.)&#10;A) 63 new cases&#10;B) 31 new cases&#10;C) 16 new cases&#10;D) 125 new cases

Accepted Answer

The answer of Solve the problem.&#10;Doctors predict that by administering...

Question 31

Given are the first three terms of a sequence that is arithmetic. Find a1 and d.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 32

Find the first five terms of the sequence. Round each term to four decimal places as necessary.&#10;

Accepted Answer

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

Question 33

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 34

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 35

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 36

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 37

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given.&#10;

Accepted Answer

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

Question 38

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 39

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given.&#10;

Accepted Answer

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

Question 40

Given are the first three terms of a sequence that is arithmetic. Find a1 and d.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 41

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 42

Given are the first three terms of a sequence that is geometric. Find a1 and r.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 43

Given are the first three terms of a sequence that is arithmetic. Find a1 and d.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 44

Find the indicated term of the sequence.&#10;The fourth term of the geometric sequence whose first term is 9 and whose common ratio is -2&#10;A) 144&#10;B) -8&#10;C) 72&#10;D) -72

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;The...

Question 45

Find the indicated term of the sequence.&#10;The fifth term of the geometric sequence 4, -20, 100, ...&#10;A) -12,500&#10;B) 625&#10;C) -2500&#10;D) 2500

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;The...

Question 46

Find the indicated term of the sequence.&#10;The sixth term of the geometric sequence 4, 20, 100, ...&#10;A) 3125&#10;B) 100&#10;C) 12,500&#10;D) 62,500

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;The...

Question 47

Given are the first three terms of a sequence that is geometric. Find a1 and r.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 48

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 49

Write the first five terms of the geometric sequence whose first term, a1, and common ratio, r, are given.&#10;

Accepted Answer

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

Question 50

Write the first five terms of the geometric sequence whose first term, a1, and common ratio, r, are given.&#10;

Accepted Answer

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

Question 51

Write the first five terms of the geometric sequence whose first term, a1, and common ratio, r, are given.&#10;

Accepted Answer

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

Question 52

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 53

Given are the first three terms of a sequence that is geometric. Find a1 and r.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 54

Given are the first three terms of a sequence that is arithmetic. Find a1 and d.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 55

Given are the first three terms of a sequence that is geometric. Find a1 and r.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 56

Given are the first three terms of a sequence that is geometric. Find a1 and r.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 57

Given are the first three terms of a sequence that is arithmetic. Find a1 and d.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 58

Find the indicated term of the sequence.&#10;The fourth term of the geometric sequence whose first term is 6 and whose common ratio is 2&#10;A) 48&#10;B) 8&#10;C) 96&#10;D) 36

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;The...

Question 59

Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1&#10;and d. If a sequence is geometric, find a1 and r.&#10;

Accepted Answer

The answer of Given are the first three terms of...

Question 60

Find the indicated term of the sequence.&#10;

Accepted Answer

The answer of Find the indicated term of the sequence.&#10;...

Question 61

Evaluate the expression.&#10;

Accepted Answer

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

Question 62

Write the series with summation notation.&#10;

Accepted Answer

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

Question 63

Solve the problem.&#10;

Accepted Answer

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

Question 64

Solve the problem.&#10;

Accepted Answer

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

Deck 14: Sequences, Series, and the Binomial Theorem