Question 1

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)   $\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$

Accepted Answer

A)  $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n } }$ 
B)  $a _ { n } = \frac { 4 ^ { n - 1 } } { 5 ^ { n - 1 } }$ 
C)  $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n + 1 } }$ 
D)  $a _ { n } = \frac { 4 ^ { n } } { 5 ^ { n } }$ 
E)  $a _ { n } = \frac { 4 ^ { n + 1 } } { 5 ^ { n } }$

Question 2

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$

Accepted Answer

A)  $a _ { n } = 3 n ^ { 2 } + 3$ 
B)  $a _ { n } = 3 n ^ { 2 } - 5 n + 3$ 
C)  $a _ { n } = 3 n ^ { 2 } - 3 n + 3$ 
D)  $a _ { n } = 3 n ^ { 2 } - 3 n + 5$ 
E)  $a _ { n } = n ^ { 2 } + 5 n + 3$

Question 3

If the statement P1  is true but the true statement P6 does not imply that the statement P7 is true, then Pn is not Necessarily true for all positive integers n.

Accepted Answer

A) True 
 B)False

Question 4

Evaluate the sum.   $\sum _ { k = 1 } ^ { 6 } 5 k$

Accepted Answer

A) 105 
B) 97 
C) 30 
D) 28 
E) 210

Question 5

A deposit of $ 5000 is made in an account that earns 8 % interest compounded monthly.The balance in the account after n months is given by $A _ { n } = 5000 \left( 1 + \frac { 0.08 } { 12 } \right) ^ { n } , n = 1,2,3 , \ldots$ Find the balance in the account after 8 years by finding the 96th term of the sequence.Round to the nearest penny.

Accepted Answer

A) $ 8,084,450.96 
B) $ 9462.29 
C) $ 9399.62 
D) $ 483200.00 
E) $ 9525.37

Question 6

Use the Binomial Theorem to expand and simplify the expression.   $( y - 3 ) ^ { 5 }$

Accepted Answer

A)  $y ^ { 5 } - 15 y ^ { 4 } + 90 y ^ { 3 } - 270 y ^ { 2 } + 405 y - 243$ 
B)  $y ^ { 5 } - 15 y ^ { 4 } - 90 y ^ { 3 } - 270 y ^ { 2 } + 405 y - 243$ 
C)  $y ^ { 5 } + 15 y ^ { 4 } - 90 y ^ { 3 } + 270 y ^ { 2 } - 405 y + 243$ 
D)  $y ^ { 5 } - 15 y ^ { 4 } + 90 y ^ { 3 } - 270 y ^ { 2 } - 405 y - 243$ 
E)  $y ^ { 5 } - 15 y ^ { 4 } - 90 y ^ { 3 } - 270 y ^ { 2 } - 405 y - 243$

Question 7

The probability that a basketball player will make a given free throw is $\frac { 6 } { 10 }$ .To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term ${ } _ { 10 } C _ { 8 } \left( \frac { 6 } { 10 } \right) ^ { 8 } \left( \frac { 4 } { 10 } \right) ^ { 2 }$ in the expansion of $\left( \frac { 6 } { 10 } + \frac { 4 } { 10 } \right) ^ { 10 }$ .Round to four decimal places.

Accepted Answer

A) 0.2721 
B) 0.0106 
C) 0.0047 
D) 0.7558 
E) 0.1209

Question 8

Find the first five terms of the geometric sequence.   $a _ { 1 } = 5 , r = 3$

Accepted Answer

A)  $5,15,45,135,405$ 
B)  $9,27,81,243,729$ 
C)  $15,45,135,405,1215$ 
D)  $1,3,9,27,81$ 
E)  $3,9,27,81,243$

Question 9

Find a formula for an  for the arithmetic sequence.  
A1 = -5, a5 = 18

Accepted Answer

A) an  = $\frac { 23 } { 4 }$ n - $\frac { 43 } { 4 }$ 
B) an  = $\frac { 23 } { 4 }$ n + 43 
C) an  = $\frac { 43 } { 4 }$ - 43n 
D) an  = $\frac { 43 } { 4 }$ + 43n 
E) an  = $\frac { 23 } { 4 }$ n + $\frac { 43 } { 4 }$

Question 10

There were approximately 42 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is 45 or older? ( $a = 42 \%$ and $b = 39 \%$ )

Accepted Answer

A)  $\frac { 1 } { 100 }$ 
B)  $\frac { 21 } { 50 }$ 
C)  $\frac { 1 } { 42 }$ 
D)  $\frac { 50 } { 21 }$ 
E) 42

Question 11

Find the coefficient a of the term in the expansion of the binomial.  $\begin{array}{lr}\text { Binominal }&\text { Terms }\
\left(x^{2}+8\right)^{12} & a x^{8}
\end{array}$

Accepted Answer

A) 8,304,721,920 
B) 8,304,721,921 
C) 8,304,721,923 
D) 8,304,721,918 
E) 8,304,721,919

Question 12

Evaluate ${ } _ { n } P _ { r }$ .   $100 P _ { 3 }$

Accepted Answer

A) 94,109,400 
B) 161,700 
C) 970,200 
D) 858,277,728,000 
E) 9,034,502,400

Question 13

Use the Binomial Theorem to expand and simplify the expression.   $( 2 x - 5 y ) ^ { 5 }$

Accepted Answer

A)  $32 x ^ { 5 } - 400 x ^ { 4 } y - 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } - 6250 x y ^ { 4 } - 3125$ 
B)  $32 x ^ { 5 } - 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } + 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } + 3125$ 
C)  $32 x ^ { 5 } + 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } - 3125$ 
D)  $32 x ^ { 5 } - 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } - 3125$ 
E)  $32 x ^ { 5 } + 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } + 3125$

Question 14

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x.) $( 5 x - 2 y ) ^ { 6 } , n = 3$

Accepted Answer

A)  $20 x ^ { 2 } y ^ { 3 }$ 
B)  $5 x ^ { 2 } y ^ { 4 }$ 
C)  $2500 x ^ { 2 } y ^ { 4 }$ 
D)  $20 x ^ { 2 } y ^ { 4 }$ 
E)  $5 x ^ { 4 } y ^ { 2 }$

Question 15

Evaluate ${ } _ { n } P _ { r }$ . 
 ${ } _ { 7 } P _ { 3 }$

Accepted Answer

A) 210 
B) 336 
C) 720 
D) 35 
E) 504

Question 16

Write the nth term of the arithmetic sequence as a function of n. ​
A1 = -7, ak + 1 = ak + 4

Accepted Answer

A) an = -3 + 4n 
B) an = -7 + 4n 
C) an = 11 - 7n. 
D) an = -3 + 4n. 
E) an = -11 + 4n

Question 17

A principal of $4000 is invested at 8% interest.Find the amount after 10 years if the interest is compounded quarterly. ​

Accepted Answer

A) $8835.16 
B) $8833.16 
C) $8836.16 
D) $8834.16 
E) $8832.16

Question 18

Find the number of diagonals of a dodecagon (12 sides).(A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

Accepted Answer

A) 24 
B) 12 
C) 144 
D) 132 
E) 54

Question 19

In how many ways can seven children posing for a photograph line up in a row? ​

Accepted Answer

A) 5,040 
B) 5,140 
C) 5,090 
D) 6,040 
E) 5,540

Question 20

Find the sum.   $\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )$

Accepted Answer

A) 85 
B) 35 
C) 26 
D) 95 
E) 55

Exam 9: Sequences Series and Probability

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$

If the statement P₁ is true but the true statement P₆ does not imply that the statement P₇ is true, then P_n is not Necessarily true for all positive integers n.

Evaluate the sum. $\sum _ { k = 1 } ^ { 6 } 5 k$

Use the Binomial Theorem to expand and simplify the expression. $( y - 3 ) ^ { 5 }$

Find the first five terms of the geometric sequence. $a _ { 1 } = 5 , r = 3$

Find a formula for a_n for the arithmetic sequence. A₁ = -5, a₅ = 18

Find the coefficient a of the term in the expansion of the binomial. $\begin{array}{lr}\text { Binominal }&\text { Terms }\\\left(x^{2}+8\right) ^{12} & a x^{8}\end{array}$

Evaluate ${ } _ { n } P _ { r }$ . $100 P _ { 3 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 x - 5 y ) ^ { 5 }$

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x.) $( 5 x - 2 y ) ^ { 6 } , n = 3$

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 7 } P _ { 3 }$

Write the nth term of the arithmetic sequence as a function of n. A₁ = -7, ak_{+ 1} = a_k + 4

A principal of $4000 is invested at 8% interest.Find the amount after 10 years if the interest is compounded quarterly.

Find the number of diagonals of a dodecagon (12 sides) .(A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

In how many ways can seven children posing for a photograph line up in a row?

Find the sum. $\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )$

Exam 9: Sequences Series and Probability

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 15,425,16125,64625\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }51​,254​,12516​,62564​

Find a quadratic model for the sequence with the indicated terms. a0=3,a1=1,a4=31a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31a0​=3,a1​=1,a4​=31

If the statement P1 is true but the true statement P6 does not imply that the statement P7 is true, then Pn is not Necessarily true for all positive integers n.

Evaluate the sum. ∑k=165k\sum _ { k = 1 } ^ { 6 } 5 k∑k=16​5k

Use the Binomial Theorem to expand and simplify the expression. (y−3) 5( y - 3 ) ^ { 5 }(y−3) 5

Find the first five terms of the geometric sequence. a1=5,r=3a _ { 1 } = 5 , r = 3a1​=5,r=3

Find a formula for an for the arithmetic sequence. A1 = -5, a5 = 18

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (x2+8) 12ax8\begin{array}{lr}\text { Binominal }&\text { Terms }\\\left(x^{2}+8\right) ^{12} & a x^{8}\end{array} Binominal (x2+8) 12​ Terms ax8​

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ . 100P3100 P _ { 3 }100P3​

Use the Binomial Theorem to expand and simplify the expression. (2x−5y) 5( 2 x - 5 y ) ^ { 5 }(2x−5y) 5

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x.) (5x−2y) 6,n=3( 5 x - 2 y ) ^ { 6 } , n = 3(5x−2y) 6,n=3

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ . 7P3{ } _ { 7 } P _ { 3 }7​P3​

Write the nth term of the arithmetic sequence as a function of n. ​ A1 = -7, ak + 1 = ak + 4

A principal of $4000 is invested at 8% interest.Find the amount after 10 years if the interest is compounded quarterly. ​

Find the number of diagonals of a dodecagon (12 sides) .(A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

In how many ways can seven children posing for a photograph line up in a row? ​

Find the sum. ∑i=15(6i+1) \sum _ { i = 1 } ^ { 5 } ( 6 i + 1 ) ∑i=15​(6i+1)

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $\frac { 1 } { 5 } , \frac { 4 } { 25 } , \frac { 16 } { 125 } , \frac { 64 } { 625 }$

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$

If the statement P₁ is true but the true statement P₆ does not imply that the statement P₇ is true, then P_n is not Necessarily true for all positive integers n.

Evaluate the sum. $\sum _ { k = 1 } ^ { 6 } 5 k$

Use the Binomial Theorem to expand and simplify the expression. $( y - 3 ) ^ { 5 }$

Find the first five terms of the geometric sequence. $a _ { 1 } = 5 , r = 3$

Find a formula for a_n for the arithmetic sequence. A₁ = -5, a₅ = 18

Find the coefficient a of the term in the expansion of the binomial. $\begin{array}{lr}\text { Binominal }&\text { Terms }\\\left(x^{2}+8\right) ^{12} & a x^{8}\end{array}$

Evaluate ${ } _ { n } P _ { r }$ . $100 P _ { 3 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 x - 5 y ) ^ { 5 }$

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x.) $( 5 x - 2 y ) ^ { 6 } , n = 3$

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 7 } P _ { 3 }$

Write the nth term of the arithmetic sequence as a function of n. A₁ = -7, ak_{+ 1} = a_k + 4

A principal of $4000 is invested at 8% interest.Find the amount after 10 years if the interest is compounded quarterly.

In how many ways can seven children posing for a photograph line up in a row?

Find the sum. $\sum _ { i = 1 } ^ { 5 } ( 6 i + 1 )$