Question 1

Evaluate the expression.
-$\sum _ { i = 1 } ^ { 5 } ( i - 10 )$

Accepted Answer

A)  $- 5$ 
B)  $- 14$ 
C)  $- 35$ 
D)  $- 30$ 
A)  $- 5$ 
B)  $- 14$ 
C)  $- 35$ 
D)  $- 30$

Question 2

Solve the problem.
-Write $0.15 \overline { 15 }$ as an infinite geometric series and use the formula for $\mathrm { S } _ { \infty }$ to write it as a rational number.

Accepted Answer

A)  $\frac { 5 } { 33 }$ 
B)  $\frac { 500 } { 33 }$ 
C)  $\frac { 3 } { 200 }$ 
D)  $\frac { 3 } { 20 }$ 
A)  $\frac { 5 } { 33 }$ 
B)  $\frac { 500 } { 33 }$ 
C)  $\frac { 3 } { 200 }$ 
D)  $\frac { 3 } { 20 }$

Question 3

Use the binomial formula to expand the binomial.
-$( 2 x + y ) ^ { 6 }$

Accepted Answer

A)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
B)  $2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
C)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
A)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
B)  $2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }$ 
C)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
D)  $64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }$

Question 4

Solve the problem.
-Jarrod has a choice between two job offers. Job A has an annual starting salary of $\$ 20,000$ with guaranteed annual raises of $\$ 700$ for the next four years, while Job B has an annual starting salary of $\$ 19,000$ with guaranteed annual raises of $\$ 2600$ for the next four years. Compare the fifth partial sums for each sequence to determine which job would pay Jarrod more over the next 5 years.

Accepted Answer

A)  Job B pays $\$ 22,500$ more over the next 5 years. 
B)  Job B pays $\$ 14,000$ more over the next 5 years. 
C)  Job A pays $\$ 1000$ more over the next 5 years. 
D)  Job A pays $\$ 7400$ more over the next 5 years. 
A)  Job B pays $\$ 22,500$ more over the next 5 years. 
B)  Job B pays $\$ 14,000$ more over the next 5 years. 
C)  Job A pays $\$ 1000$ more over the next 5 years. 
D)  Job A pays $\$ 7400$ more over the next 5 years.

Question 5

Find the indicated term of the sequence.
-The eighth term of the arithmetic sequence whose first term is $- 6$ and whose common difference is $- 4$

Accepted Answer

A)  26 
B)  $- 38$ 
C)  22 
D)  $- 34$ 
A)  26 
B)  $- 38$ 
C)  22 
D)  $- 34$

Question 6

Given are the first three terms of a sequence that is geometric. Find a1 and r.
-$\mathrm { z } , - 11 \mathrm { z } , 121 \mathrm { z }$

Accepted Answer

A)  $a _ { 1 } = z ; d = - 11$ 
B)  $a _ { 1 } = z ; r = - 11$ 
C)  $a _ { 1 } = z ; r = 11$ 
D)  $a _ { 1 } = z ; r = - 11 z$ 
A)  $a _ { 1 } = z ; d = - 11$ 
B)  $a _ { 1 } = z ; r = - 11$ 
C)  $a _ { 1 } = z ; r = 11$ 
D)  $a _ { 1 } = z ; r = - 11 z$

Question 7

Find the indicated term for the sequence whose general term is given.
-$a _ { n } = 2^ n ; a _ { 3 }$

Accepted Answer

A)  6 
B)  4 
C)  9 
D)  8 
A)  6 
B)  4 
C)  9 
D)  8

Question 8

Use the partial sum formula to find the partial sum of the given geometric sequence.
-Find the sum of the first five terms of the geometric sequence $1,4,16 , \ldots$

Accepted Answer

A)  343 
B)  345 
C)  331 
D)  341 
A)  343 
B)  345 
C)  331 
D)  341

Question 9

Use the binomial formula to expand the binomial.
-$\left( 4 x ^ { 2 } + 1 \right) ^ { 3 }$

Accepted Answer

A)  $64 x ^ { 6 } + 48 x ^ { 4 } + 12 x ^ { 2 } + 1$ 
B)  $64 x ^ { 3 } + 48 x ^ { 2 } + 12 x + 1$ 
C)  $256 x ^ { 8 } + 64 x ^ { 6 } + 48 x ^ { 4 } + 12 x ^ { 2 } + 1$ 
D)  $\left( 16 x ^ { 4 } + 8 x ^ { 2 } + 1 \right) ^ { 3 }$ 
A)  $64 x ^ { 6 } + 48 x ^ { 4 } + 12 x ^ { 2 } + 1$ 
B)  $64 x ^ { 3 } + 48 x ^ { 2 } + 12 x + 1$ 
C)  $256 x ^ { 8 } + 64 x ^ { 6 } + 48 x ^ { 4 } + 12 x ^ { 2 } + 1$ 
D)  $\left( 16 x ^ { 4 } + 8 x ^ { 2 } + 1 \right) ^ { 3 }$

Question 10

Solve the problem.
-A lecture hall has 11 rows with 14 seats in the first row, 18 seats in the second row, 22 seats in the third row, and so on. Write an equation of a sequence whose terms correspond to the seats in each row. Find the number of seats in the seventh row.

Accepted Answer

A)  $a _ { n } = 14 + 4 n ; 42$ seats 
B)  $a _ { n } = 18 ( n - 1 ) ; 108$ seats 
C)  $a _ { n } = 14 + 4 ( n - 1 ) ; 38$ seats 
D)  $a _ { n } = 14 + 4 ( 11 - n ) ; 30$ seats 
A)  $a _ { n } = 14 + 4 n ; 42$ seats 
B)  $a _ { n } = 18 ( n - 1 ) ; 108$ seats 
C)  $a _ { n } = 14 + 4 ( n - 1 ) ; 38$ seats 
D)  $a _ { n } = 14 + 4 ( 11 - n ) ; 30$ seats

Question 11

Solve the problem.
-If $\mathrm { a } _ { 1 }$ is $- 10$ and $\mathrm { d }$ is 3 , find $\mathrm { S } _ { 55 }$.

Accepted Answer

A)  3625 
B)  3905 
C)  3834 
D)  3988 
A)  3625 
B)  3905 
C)  3834 
D)  3988

Question 12

Given are the first three terms of a sequence that is arithmetic. Find a1 and d.
-9, 13, 17

Accepted Answer

A)  $a _ { 1 } = 9 ; d = - 12$ 
B)  $\mathrm { a } _ { 1 } = 9 ; \mathrm { d } = 12$ 
C)  $a _ { 1 } = 9 ; d = - 4$ 
D)  $a _ { 1 } = 9 ; d = 4$ 
A)  $a _ { 1 } = 9 ; d = - 12$ 
B)  $\mathrm { a } _ { 1 } = 9 ; \mathrm { d } = 12$ 
C)  $a _ { 1 } = 9 ; d = - 4$ 
D)  $a _ { 1 } = 9 ; d = 4$

Question 13

Write the series with summation notation.
-$( - 1 ) + 4 + ( - 9 ) + 16 + ( - 25 ) + 36$

Accepted Answer

A)  $\sum _ { \mathrm { i } = 1 } ^ { 6 } ( - 1 ) ^ { ( \mathrm { i } + 1 ) \cdot \mathrm { i } ^ { 2 } }$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 6 } ( - 1 ) ^ { \mathrm { i } } \cdot \mathrm { i } ^ { 2 }$ 
C)  $\sum _ { i = 1 } ^ { 6 } - i ^ { 2 }$ 
D)  $\sum _ { i = 1 } ^ { 6 } ( - i ) ^ { 2 }$ 
A)  $\sum _ { \mathrm { i } = 1 } ^ { 6 } ( - 1 ) ^ { ( \mathrm { i } + 1 ) \cdot \mathrm { i } ^ { 2 } }$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 6 } ( - 1 ) ^ { \mathrm { i } } \cdot \mathrm { i } ^ { 2 }$ 
C)  $\sum _ { i = 1 } ^ { 6 } - i ^ { 2 }$ 
D)  $\sum _ { i = 1 } ^ { 6 } ( - i ) ^ { 2 }$

Question 14

Write the first five terms of the sequence whose general term is given.
-$a _ { n } = 2 ^ { n }$

Accepted Answer

A)  $2,4,8,16,32$ 
B)  $4,8,16,32,64$ 
C)  $1,2,4,8,16$ 
D)  $1,4,9,16,25$ 
A)  $2,4,8,16,32$ 
B)  $4,8,16,32,64$ 
C)  $1,2,4,8,16$ 
D)  $1,4,9,16,25$

Question 15

Solve the problem.
-Write $0.77 \overline { 7 }$ as an infinite geometric series and use the formula for $\mathrm { S } _ { \infty }$ to write it as a rational number.

Accepted Answer

A)  $\frac { 7 } { 100 }$ 
B)  $\frac { 7 } { 10 }$ 
C)  $\frac { 70 } { 9 }$ 
D)  $\frac { 7 } { 9 }$ 
A)  $\frac { 7 } { 100 }$ 
B)  $\frac { 7 } { 10 }$ 
C)  $\frac { 70 } { 9 }$ 
D)  $\frac { 7 } { 9 }$

Question 16

Find the partial sum.
-Find the sum of the first five terms of the sequence whose general terms is $\mathrm { a } _ { \mathrm { n } } = - 9 \mathrm { n }$.

Accepted Answer

A)  $- 27$ 
B)  $- 135$ 
C)  $- 90$ 
D)  135 
A)  $- 27$ 
B)  $- 135$ 
C)  $- 90$ 
D)  135

Question 17

Evaluate the expression.
-$\frac { 5 ! } { 3 ! 2 ! }$

Accepted Answer

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

Question 18

Find the indicated term of the sequence.
-The fourth term of the geometric sequence whose first term is 9 and whose common ratio is -2

Accepted Answer

A)  144 
B)  -8 
C)  72 
D)  -72 
A)  144 
B)  -8 
C)  72 
D)  -72

Question 19

Write the first five terms of the geometric sequence whose first term, a1, and common ratio, r, are given.
-$a _ { 1 } = - 7 ; r = 4$

Accepted Answer

A)  $- 28 , - 112 , - 448 , - 1792 , - 7168$ 
B)  $- 7 , - 28 , - 112 , - 448 , - 1792$ 
C)  $- 7 , - 3,1,5,9$ 
D)  $- 7,28 , - 112,448 , - 1792$ 
A)  $- 28 , - 112 , - 448 , - 1792 , - 7168$ 
B)  $- 7 , - 28 , - 112 , - 448 , - 1792$ 
C)  $- 7 , - 3,1,5,9$ 
D)  $- 7,28 , - 112,448 , - 1792$

Question 20

Write the series with summation notation.
-$4 + 16 + 36 + 64 + 100$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 5 } 4 i$ 
B)  $\sum _ { i = 1 } ^ { 5 } 16 i$ 
C)  $\sum _ { i = 1 } ^ { 5 } 16 i ^ { 2 }$ 
D)  $\sum _ { i = 1 } ^ { 5 } 4 i ^ { 2 }$ 
A)  $\sum _ { i = 1 } ^ { 5 } 4 i$ 
B)  $\sum _ { i = 1 } ^ { 5 } 16 i$ 
C)  $\sum _ { i = 1 } ^ { 5 } 16 i ^ { 2 }$ 
D)  $\sum _ { i = 1 } ^ { 5 } 4 i ^ { 2 }$

Evaluate the expression. - $\sum _ { i = 1 } ^ { 5 } ( i - 10 )$

Solve the problem. -Write $0.15 \overline { 15 }$ as an infinite geometric series and use the formula for $\mathrm { S } _ { \infty }$ to write it as a rational number.

Use the binomial formula to expand the binomial. - $( 2 x + y ) ^ { 6 }$

Find the indicated term of the sequence. -The eighth term of the arithmetic sequence whose first term is $- 6$ and whose common difference is $- 4$

Given are the first three terms of a sequence that is geometric. Find a1 and r. - $\mathrm { z } , - 11 \mathrm { z } , 121 \mathrm { z }$

Find the indicated term for the sequence whose general term is given. - $a _ { n } = 2^ n ; a _ { 3 }$

Use the partial sum formula to find the partial sum of the given geometric sequence. -Find the sum of the first five terms of the geometric sequence $1,4,16 , \ldots$

Use the binomial formula to expand the binomial. - $\left( 4 x ^ { 2 } + 1 \right) ^ { 3 }$

Solve the problem. -A lecture hall has 11 rows with 14 seats in the first row, 18 seats in the second row, 22 seats in the third row, and so on. Write an equation of a sequence whose terms correspond to the seats in each row. Find the number of seats in the seventh row.

Solve the problem. -If $\mathrm { a } _ { 1 }$ is $- 10$ and $\mathrm { d }$ is 3 , find $\mathrm { S } _ { 55 }$ .

Given are the first three terms of a sequence that is arithmetic. Find a1 and d. -9, 13, 17

Write the series with summation notation. - $( - 1 ) + 4 + ( - 9 ) + 16 + ( - 25 ) + 36$

Write the first five terms of the sequence whose general term is given. - $a _ { n } = 2 ^ { n }$

Solve the problem. -Write $0.77 \overline { 7 }$ as an infinite geometric series and use the formula for $\mathrm { S } _ { \infty }$ to write it as a rational number.

Find the partial sum. -Find the sum of the first five terms of the sequence whose general terms is $\mathrm { a } _ { \mathrm { n } } = - 9 \mathrm { n }$ .

Evaluate the expression. - $\frac { 5 ! } { 3 ! 2 ! }$

Find the indicated term of the sequence. -The fourth term of the geometric sequence whose first term is 9 and whose common ratio is -2

Write the first five terms of the geometric sequence whose first term, a1, and common ratio, r, are given. - $a _ { 1 } = - 7 ; r = 4$

Write the series with summation notation. - $4 + 16 + 36 + 64 + 100$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Filters

Exam 14: Sequences, Series, and the Binomial Theorem

Evaluate the expression. - ∑i=15(i−10)\sum _ { i = 1 } ^ { 5 } ( i - 10 )∑i=15​(i−10)

Solve the problem. -Write 0.1515‾0.15 \overline { 15 }0.1515 as an infinite geometric series and use the formula for S∞\mathrm { S } _ { \infty }S∞​ to write it as a rational number.

Use the binomial formula to expand the binomial. - (2x+y)6( 2 x + y ) ^ { 6 }(2x+y)6

Find the indicated term of the sequence. -The eighth term of the arithmetic sequence whose first term is −6- 6−6 and whose common difference is −4- 4−4

Given are the first three terms of a sequence that is geometric. Find a1 and r. - z,−11z,121z\mathrm { z } , - 11 \mathrm { z } , 121 \mathrm { z }z,−11z,121z

Find the indicated term for the sequence whose general term is given. - an=2n;a3a _ { n } = 2^ n ; a _ { 3 }an​=2n;a3​

Use the partial sum formula to find the partial sum of the given geometric sequence. -Find the sum of the first five terms of the geometric sequence 1,4,16,…1,4,16 , \ldots1,4,16,…

Use the binomial formula to expand the binomial. - (4x2+1)3\left( 4 x ^ { 2 } + 1 \right) ^ { 3 }(4x2+1)3