Question 1

Write the expression for the general (or nth)term,rm, $a _ { n },$ , of the arithmetic sequence.
-$a _ { 1 } = \frac { 6 } { 5 } , d = - \frac { 1 } { 5 }$

Accepted Answer

A)  $a _ { n } = - \frac { 1 } { 5 } n + \frac { 6 } { 5 }$ 
B)  $$a _ { n } = \frac { 6 } { 5 } n - \frac { 7 } { 5 }$$ 
C)  $$a _ { n } = - \frac { 1 } { 5 } n + \frac { 7 } { 5 }$$ 
D)  $a _ { n } = \frac { 6 } { 5 } n - \frac { 1 } { 5 }$

Question 2

Evaluate the expression.
-$\frac { 10 ! } { ( 10 - 7 ) ! }$

Accepted Answer

A) 720 
B)  $\frac { 10 } { 7 }$ 
C)  $\frac { 10 } { 3 }$ 
D) 604,800

Question 3

Solve the problem.
-The odds in favor of an event are 5:4. i)Find the probability that the event occurs.
Ii)Find the probability that the event does not occur.

Accepted Answer

A)  i) $\frac { 9 } { 5 }$

ii) $\frac { 9 } { 4 }$ 
B)  i) $\frac { 9 } { 4 }$

ii) $\frac { 9 } { 5 }$ 
C)  i) $\frac { 4 } { 9 }$

ii) $\frac { 5 } { 9 }$ 
D)  i) $\frac { 5 } { 9 }$

ii) $\frac { 4 } { 9 }$

Question 4

Find the indicated quantity of the arithmetic sequence.
-a1 = -6 , d = 1 ; find $\mathrm { a } _ { 40 }$

Accepted Answer

A) 34 
B) 33 
C) -45 
D) -46

Question 5

Find the indicated term of the sequence whose nth term is shown.
-$a _ { n } = n ( n - 1 ) , \quad \text { eighth term }$

Accepted Answer

A) 240 
B) 224 
C) 256 
D) 16

Question 6

For the geometric sequence, find the common ratio, r.
-$\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1024 } , \ldots$

Accepted Answer

A) 4 
B) 40 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 40 }$

Question 7

Solve the problem.
-A marble is taken out of a bag containing 90 marbles: 20 red, 15 blue, 25 green, and 30 orange. Find the probability: P(a blue marble is chosen)

Accepted Answer

A)  $\frac { 1 } { 6 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 2 } { 9 }$ 
D)  $\frac { 13 } { 18 }$

Question 8

Evaluate the combination.
-$\left( \begin{array} { l } 
4 \
4
\end{array} \right)$

Accepted Answer

A) 0 
B) 1 
C) 24 
D) 2

Question 9

Evaluate the expression.
-$7 !$

Accepted Answer

A) 5040 
B) 10,080 
C) 2520 
D) 720

Question 10

Write the first three terms of the expansion.
-$( x + 3 ) ^ { 20 }$

Accepted Answer

A)  $x ^ { 20 } + 60 x ^ { 19 } - 1710 x ^ { 18 }$ 
B)  $x ^ { 20 } + 1710 x ^ { 19 } + 1710 x ^ { 18 }$ 
C)  $x ^ { 20 } + 570 x ^ { 19 } + 1710 x ^ { 18 }$ 
D)  $x ^ { 20 } + 60 x ^ { 19 } + 1710 x ^ { 18 }$

Question 11

Solve the problem.
-A card is selected at random from a deck of cards. Find the probability: P(selecting a 10)

Accepted Answer

A)  $\frac { 1 } { 52 }$ 
B)  $\frac { 11 } { 13 }$ 
C)  $\frac { 1 } { 13 }$ 
D)  $\frac { 15 } { 52 }$

Question 12

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.
-$a = 5 , d = - 5 ; \quad \text { find } a _ { n } \text { and } a _ { 15 }$

Accepted Answer

A)  $a _ { n } = 10 + 5 n , a _ { 15 } = - 65$ 
B)  $a _ { n } = 10 - 5 n , a _ { 15 } = - 65$ 
C)  $a _ { n } = 10 - 5 n , a _ { 15 } = - 25$ 
D)  $a _ { n } = 5 - 5 n , a _ { 15 } = - 65$

Question 13

Use the binomial theorem to expand the expression.
-$( 4 x + 3 ) ^ { 3 }$

Accepted Answer

A)  $16 x ^ { 2 } + 24 x + 9$ 
B)  $64 x ^ { 3 } + 144 x ^ { 2 } + 108 x + 27$ 
C)  $64 x ^ { 3 } + 144 x ^ { 2 } + 144 x + 27$ 
D)  $16 x ^ { 6 } + 12 x ^ { 3 } + 729$

Question 14

Solve the problem.
-A license plate is to consist of 6 digits followed by 2 letters. Determine the number of different license plates possible if the first and fifth digits must be odd, and repetition is not permitted.

Accepted Answer

A) 27,300,000 
B) 2350 
C) 109,200,000 
D) 21,840,000

Question 15

For the geometric sequence, find the common ratio, r.
-$\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$

Accepted Answer

A) 12 
B) 4 
C) 10 
D)  $\frac { 1 } { 4 }$

Question 16

Write the next three terms of the sequence.
-3, 1, -1, -3, ...

Accepted Answer

A) -5, -7, -9 
B) -1, 1, 3 
C) 5, 7, 9 
D) -7, -9, -11

Question 17

Find the indicated quantity of the arithmetic sequence.
-a1 = -5, d = -8; find $\mathrm { a } _ { 5 }$

Accepted Answer

A) 27 
B) -37 
C) -45 
D) 37

Question 18

Evalutate the series.
-$$\sum _ { n = 2 } ^ { 5 } ( 3 n - 3 )$$

Accepted Answer

A) 27 
B) 24 
C) 30 
D) 18

Question 19

Solve the problem.
-In a geometric series, $a _ { 2 } = - 12 \text { and } a _ { 5 } = 96;$ ; find r and ; find r anda1.

Accepted Answer

The answer of Solve the problem.
-In a geometric series, \(a...

Question 20

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-$- \frac { 1 } { 3 } , - \frac { 1 } { 27 } , - \frac { 1 } { 243 } , - \frac { 1 } { 2187 } , \ldots$

Accepted Answer

A)  $a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n - 1 } + \frac { 8 } { 27 }$ 
B)  $a _ { n } = - \frac { 1 } { 3 } + \frac { 8 } { 27 } ( n - 1 )$ 
C)  $a _ { n } = - \frac { 1 } { 3 } + \frac { 1 } { 9 } ( n - 1 )$ 
D)  $a _ { n } = - \frac { 1 } { 3 } \left( \frac { 1 } { 9 } \right) ^ { n - 1 }$

Exam 12: Sequences, Series, and Probability

Write the expression for the general (or nth) term,rm, $a _ { n },$ , of the arithmetic sequence. - $a _ { 1 } = \frac { 6 } { 5 } , d = - \frac { 1 } { 5 }$

Evaluate the expression. - $\frac { 10 ! } { ( 10 - 7 ) ! }$

Solve the problem. -The odds in favor of an event are 5:4. i) Find the probability that the event occurs. Ii) Find the probability that the event does not occur.

Find the indicated quantity of the arithmetic sequence. -a1 = -6 , d = 1 ; find $\mathrm { a } _ { 40 }$

Find the indicated term of the sequence whose nth term is shown. - $a _ { n } = n ( n - 1 ) , \quad \text { eighth term }$

For the geometric sequence, find the common ratio, r. - $\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1024 } , \ldots$

Solve the problem. -A marble is taken out of a bag containing 90 marbles: 20 red, 15 blue, 25 green, and 30 orange. Find the probability: P(a blue marble is chosen)

Evaluate the combination. - $\left( \begin{array} { l } 4 \\4\end{array} \right)$

Evaluate the expression. - $7 !$

Write the first three terms of the expansion. - $( x + 3 ) ^ { 20 }$

Solve the problem. -A card is selected at random from a deck of cards. Find the probability: P(selecting a 10)

Write the expression for the general (or nth) term, an, of the arithmetic sequence. Then, find the indicated term of the arithmetic sequence. - $a = 5 , d = - 5 ; \quad \text { find } a _ { n } \text { and } a _ { 15 }$

Use the binomial theorem to expand the expression. - $( 4 x + 3 ) ^ { 3 }$

Solve the problem. -A license plate is to consist of 6 digits followed by 2 letters. Determine the number of different license plates possible if the first and fifth digits must be odd, and repetition is not permitted.

For the geometric sequence, find the common ratio, r. - $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$

Write the next three terms of the sequence. -3, 1, -1, -3, ...

Find the indicated quantity of the arithmetic sequence. -a1 = -5, d = -8; find $\mathrm { a } _ { 5 }$

Evalutate the series. - $\sum _ { n = 2 } ^ { 5 } ( 3 n - 3 )$

Solve the problem. -In a geometric series, $a _ { 2 } = - 12 \text { and } a _ { 5 } = 96;$ ; find r and ; find r anda1.

Write the expression for the general (or nth) termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. - $- \frac { 1 } { 3 } , - \frac { 1 } { 27 } , - \frac { 1 } { 243 } , - \frac { 1 } { 2187 } , \ldots$

Exam 12: Sequences, Series, and Probability

Write the expression for the general (or nth) term,rm, an,a _ { n },an​, , of the arithmetic sequence. - a1=65,d=−15a _ { 1 } = \frac { 6 } { 5 } , d = - \frac { 1 } { 5 }a1​=56​,d=−51​

Evaluate the expression. - 10!(10−7) !\frac { 10 ! } { ( 10 - 7 ) ! }(10−7) !10!​

Solve the problem. -The odds in favor of an event are 5:4. i) Find the probability that the event occurs. Ii) Find the probability that the event does not occur.

Find the indicated quantity of the arithmetic sequence. -a1 = -6 , d = 1 ; find a40\mathrm { a } _ { 40 }a40​

Find the indicated term of the sequence whose nth term is shown. - an=n(n−1) , eighth term a _ { n } = n ( n - 1 ) , \quad \text { eighth term }an​=n(n−1) , eighth term

For the geometric sequence, find the common ratio, r. - 34,316,364,3256,31024,…\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \frac { 3 } { 256 } , \frac { 3 } { 1024 } , \ldots43​,163​,643​,2563​,10243​,…

Solve the problem. -A marble is taken out of a bag containing 90 marbles: 20 red, 15 blue, 25 green, and 30 orange. Find the probability: P(a blue marble is chosen)

Evaluate the combination. - (44) \left( \begin{array} { l } 4 \\4\end{array} \right) (44​)

Evaluate the expression. - 7!7 !7!

Write the first three terms of the expansion. - (x+3) 20( x + 3 ) ^ { 20 }(x+3) 20