Question 1

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are
given.
-$$\begin{array} { l } 
\mathrm { a } = 9 ; \mathrm { d } = 4 \
\mathrm { a } _ { \mathrm { n } } = ? ; \mathrm { a } _ { 14 } = ?
\end{array}$$

Accepted Answer

A)  $a _ { n } = 5 - 4 n ; a _ { 14 } = 61$ 
B)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 61$ 
C)  $a _ { n } = 9 + 4 n ; a _ { 14 } = 61$ 
D)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 29$ 
A)  $a _ { n } = 5 - 4 n ; a _ { 14 } = 61$ 
B)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 61$ 
C)  $a _ { n } = 9 + 4 n ; a _ { 14 } = 61$ 
D)  $a _ { n } = 5 + 4 n ; a _ { 14 } = 29$

Question 2

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-$$\mathrm { a } = 5 ; \mathrm { r } = 3 \pi$$

Accepted Answer

A)  $a _ { 5 } = 405 \pi , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi$ 
B)  $a _ { 5 } = 1,215 \pi ^ { 5 } , a _ { n } = 5 \cdot 3 ^ { n } \pi ^ { n }$ 
C)  $a _ { 5 } = 5 + 12 \pi , a _ { n } = 5 + 3 \pi ( n - 1 )$ 
D)  a5 $= 405 \pi ^ { 4 } , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi ^ { n - 1 }$ 
A)  $a _ { 5 } = 405 \pi , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi$ 
B)  $a _ { 5 } = 1,215 \pi ^ { 5 } , a _ { n } = 5 \cdot 3 ^ { n } \pi ^ { n }$ 
C)  $a _ { 5 } = 5 + 12 \pi , a _ { n } = 5 + 3 \pi ( n - 1 )$ 
D)  a5 $= 405 \pi ^ { 4 } , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi ^ { n - 1 }$

Question 3

Solve the problem.
-A baseball player signs a contract with a starting salary of $840,000 per year and an annual increase of 4.5% beginning in the second year. What will the athlete's salary be, to the nearest dollar, in the sixth year?

Accepted Answer

A)  $1,048,864 
B)  $1,045,321 
C)  $1,046,793 
D)  $1,047,440 
A)  $1,048,864 
B)  $1,045,321 
C)  $1,046,793 
D)  $1,047,440

Question 4

Solve the problem.
-A ping-pong ball is dropped from a height of 9 ft and always rebounds $\frac { 1 } { 3 }$ of the distance fallen. Find the total sum of the rebound heights of the ball.

Accepted Answer

A)  3 ft 
B)  6 ft 
C)  4.5 ft 
D)  13.5 ft 
A)  3 ft 
B)  6 ft 
C)  4.5 ft 
D)  13.5 ft

Question 5

Write out the first five terms of the sequence.
-{4n - 2}

Accepted Answer

A)  6, 10, 14, 18, 22 
B)  2, 3, 4, 5, 6 
C)  -2, -6, -10, -14, -18 
D)  2, 6, 10, 14, 18 
A)  6, 10, 14, 18, 22 
B)  2, 3, 4, 5, 6 
C)  -2, -6, -10, -14, -18 
D)  2, 6, 10, 14, 18

Question 6

Determine whether the sequence is geometric.
-4, -12, 36, -108, 324, ...

Accepted Answer

A)  Geometric 
B)  Not geometric 
A)  Geometric 
B)  Not geometric

Question 7

Evaluate the expression.
-$$\left( \begin{array} { l } 
5 \
2
\end{array} \right)$$

Accepted Answer

A)  5 
B)  10 
C)  0 
D)  1 
A)  5 
B)  10 
C)  0 
D)  1

Question 8

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so.
-$$\frac { 1 } { 7 } , \frac { 1 } { 9 } , \frac { 1 } { 11 } , \frac { 1 } { 13 }$$

Accepted Answer

A)  2 
B)  $\frac { 1 } { 2 }$ 
C)  $2 \frac { 1 } { 2 }$ 
D)  Not geometric 
A)  2 
B)  $\frac { 1 } { 2 }$ 
C)  $2 \frac { 1 } { 2 }$ 
D)  Not geometric

Question 9

Evaluate the factorial expression.
-$$\frac { ( \mathrm { n } + 9 ) ! } { \mathrm { n } + 9 }$$

Accepted Answer

A)  $n + 9$ ! 
B)  1 
C)  $( n + 8 ) !$ 
D)  9 ! 
A)  $n + 9$ ! 
B)  1 
C)  $( n + 8 ) !$ 
D)  9 !

Question 10

Determine whether the sequence is geometric.
-7, 4, 1, -2, -5, ...

Accepted Answer

A)  Geometric 
B)  Not geometric 
A)  Geometric 
B)  Not geometric

Question 11

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-Use the Principle of Mathematical Induction to show that the statement "5 is a factor of 7n - 2n" is true for all
natural numbers. ( $$\left( \text { Hint: } 7 ^ { \mathrm { k } + 1 } - 2 ^ { \mathrm { k } + 1 } = 7 \left( 7 ^ { \mathrm { k } } - 2 ^ { \mathrm { k } } \right) + 5 \cdot 2 ^ { \mathrm { k } } \right)$$

Accepted Answer

When @#LAT-DLM& , so the statement is true when n

Question 12

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-$$\mathrm { a } = - 8 ; \mathrm { r } = - 5$$

Accepted Answer

A)  $\mathrm { a } _ { 5 } = 1,000 ; \mathrm { a } _ { \mathrm { n } } = - 8 \cdot ( - 5 ) ^ { \mathrm { n } }$ 
B)  $\mathrm { a } _ { 5 } = - 5,000 ; \mathrm { a } _ { \mathrm { n } } = - 8 \cdot ( - 5 ) ^ { \mathrm { n } }$ 
C)  $a _ { 5 } = - 5,000 ; a _ { n } = - 8 \cdot ( - 5 ) ^ { n - 1 }$ 
D)  $a _ { 5 } = 1,000 ; a _ { n } = - 8 \cdot ( - 5 ) ^ { n - 1 }$ 
A)  $\mathrm { a } _ { 5 } = 1,000 ; \mathrm { a } _ { \mathrm { n } } = - 8 \cdot ( - 5 ) ^ { \mathrm { n } }$ 
B)  $\mathrm { a } _ { 5 } = - 5,000 ; \mathrm { a } _ { \mathrm { n } } = - 8 \cdot ( - 5 ) ^ { \mathrm { n } }$ 
C)  $a _ { 5 } = - 5,000 ; a _ { n } = - 8 \cdot ( - 5 ) ^ { n - 1 }$ 
D)  $a _ { 5 } = 1,000 ; a _ { n } = - 8 \cdot ( - 5 ) ^ { n - 1 }$

Question 13

Solve.
-During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $ 192,000, then what are the profits for each of the first four years?

Accepted Answer

A)  $13,000, $26,000, $52,000, $102,000 
B)  $12,000, $24,000, $36,000, $48,000 
C)  $12,000, $24,000, $48,000, $96,000 
D)  $12,000, $24,000, $48,000, $120,000 
A)  $13,000, $26,000, $52,000, $102,000 
B)  $12,000, $24,000, $36,000, $48,000 
C)  $12,000, $24,000, $48,000, $96,000 
D)  $12,000, $24,000, $48,000, $120,000

Question 14

Find the indicated term using the given information.
-$$\mathrm { a } = 2 , \mathrm {~d} = \frac { 7 } { 5 } ; \mathrm { a } 26$$

Accepted Answer

A)  $- \frac { 172 } { 5 }$ 
B)  $\frac { 192 } { 5 }$ 
C)  $- 33$ 
D)  37 
A)  $- \frac { 172 } { 5 }$ 
B)  $\frac { 192 } { 5 }$ 
C)  $- 33$ 
D)  37

Question 15

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence
with the given first term, a1, and common ratio, r.
-$$\text { Find a } 7 \text { for the sequence } 0.7,0.07,0.007 , \ldots$$

Accepted Answer

A)  0.00000007 
B)  0.0000007 
C)  0.00000001 
D)  0.000007 
A)  0.00000007 
B)  0.0000007 
C)  0.00000001 
D)  0.000007

Question 16

Find the nth term of the geometric sequence.
-$$a = 2 ; r = - 4$$

Accepted Answer

A)  $a _ { n } = 2 \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = - 4 \cdot 2 ^ { n - 1 }$ 
C)  $a _ { n } = 2 \cdot - 4 ^ { n }$ 
D)  $a _ { n } = 2 \cdot - 4 ^ { n - 1 }$ 
A)  $a _ { n } = 2 \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = - 4 \cdot 2 ^ { n - 1 }$ 
C)  $a _ { n } = 2 \cdot - 4 ^ { n }$ 
D)  $a _ { n } = 2 \cdot - 4 ^ { n - 1 }$

Question 17

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-$\sum _ { k = 1 } ^ { 12 } \frac { 1 } { 7 } \cdot ( - 2 ) ^ { k - 1 }$

Accepted Answer

A)  -195 
B)  -195.86 
C)  -194 
D)  -195.29 
A)  -195 
B)  -195.86 
C)  -194 
D)  -195.29

Question 18

Find the indicated term using the given information.
-$$5,2 , - 1 , \ldots ; \text { a } 44$$

Accepted Answer

A)  134 
B)  -127 
C)  137 
D)  -124 
A)  134 
B)  -127 
C)  137 
D)  -124

Question 19

Evaluate the factorial expression.
-$$\frac { n ( n + 9 ) ! } { ( n + 10 ) ! }$$

Accepted Answer

A)  $\frac { n } { 10 }$ 
B)  $\frac { n } { n + 10 }$ 
C)  $\frac { \mathrm { n } } { ( \mathrm { n } + 10 ) ! }$ 
D)  $\frac { 1 } { n + 10 }$ 
A)  $\frac { n } { 10 }$ 
B)  $\frac { n } { n + 10 }$ 
C)  $\frac { \mathrm { n } } { ( \mathrm { n } + 10 ) ! }$ 
D)  $\frac { 1 } { n + 10 }$

Question 20

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of
summation.
-$$\frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 } + \frac { 7 } { 8 } + \ldots + \frac { 17 } { 18 }$$

Accepted Answer

A)  $\sum _ { k = 5 } ^ { 17 } \frac { k } { k + 1 }$ 
B)  $\sum _ { k = 4 } ^ { 17 } \frac { k + 1 } { k }$ 
C)  $\sum _ { k = 4 } ^ { 17 } \frac { k } { k + 1 }$ 
D)  $\sum _ { \mathrm { k } = 4 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } \cdot 1.5 }$ 
A)  $\sum _ { k = 5 } ^ { 17 } \frac { k } { k + 1 }$ 
B)  $\sum _ { k = 4 } ^ { 17 } \frac { k + 1 } { k }$ 
C)  $\sum _ { k = 4 } ^ { 17 } \frac { k } { k + 1 }$ 
D)  $\sum _ { \mathrm { k } = 4 } ^ { 17 } \frac { \mathrm { k } } { \mathrm { k } \cdot 1.5 }$

Find the nth term and the indicated term of the arithmetic sequence whose initial term, a, and common difference, d, are given. - =9;=4 =?;=?

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - $\mathrm { a } = 5 ; \mathrm { r } = 3 \pi$

Solve the problem. -A baseball player signs a contract with a starting salary of $840,000 per year and an annual increase of 4.5% beginning in the second year. What will the athlete's salary be, to the nearest dollar, in the sixth year?

Solve the problem. -A ping-pong ball is dropped from a height of 9 ft and always rebounds $\frac { 1 } { 3 }$ of the distance fallen. Find the total sum of the rebound heights of the ball.

Write out the first five terms of the sequence. -{4n - 2}

Determine whether the sequence is geometric. -4, -12, 36, -108, 324, ...

Evaluate the expression. - $\left( \begin{array} { l } 5 \\2\end{array} \right)$

If the sequence is geometric, find the common ratio. If the sequence is not geometric, say so. - $\frac { 1 } { 7 } , \frac { 1 } { 9 } , \frac { 1 } { 11 } , \frac { 1 } { 13 }$

Evaluate the factorial expression. - $\frac { ( \mathrm { n } + 9 ) ! } { \mathrm { n } + 9 }$

Determine whether the sequence is geometric. -7, 4, 1, -2, -5, ...

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - $\mathrm { a } = - 8 ; \mathrm { r } = - 5$

Solve. -During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $ 192,000, then what are the profits for each of the first four years?

Find the indicated term using the given information. - $\mathrm { a } = 2 , \mathrm {~d} = \frac { 7 } { 5 } ; \mathrm { a } 26$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - $\text { Find a } 7 \text { for the sequence } 0.7,0.07,0.007 , \ldots$

Find the nth term of the geometric sequence. - $a = 2 ; r = - 4$

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\sum _ { k = 1 } ^ { 12 } \frac { 1 } { 7 } \cdot ( - 2 ) ^ { k - 1 }$

Find the indicated term using the given information. - $5,2 , - 1 , \ldots ; \text { a } 44$

Evaluate the factorial expression. - $\frac { n ( n + 9 ) ! } { ( n + 10 ) ! }$

Express the sum using summation notation with a lower limit of summation not necessarily 1 and with k for the index of summation. - $\frac { 4 } { 5 } + \frac { 5 } { 6 } + \frac { 6 } { 7 } + \frac { 7 } { 8 } + \ldots + \frac { 17 } { 18 }$

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Exam 11: Sequences; Induction; the Binomial Theorem