Question 1

Find the sum of the geometric series. $$5 + 1 + \frac { 1 } { 5 } + \frac { 1 } { 25 } + \frac { 1 } { 125 }$$

Accepted Answer

A)  $\frac { 8 } { 155 }$ 
B)  $\frac { 9 } { 155 }$ 
C)  $\frac { 781 } { 125 }$ 
D)  $\frac { 9 } { 125 }$ 
A)  $\frac { 8 } { 155 }$ 
B)  $\frac { 9 } { 155 }$ 
C)  $\frac { 781 } { 125 }$ 
D)  $\frac { 9 } { 125 }$

Question 2

Find a formula for the nth term of the sequence. $$\frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 } , \ldots$$

Accepted Answer

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

Question 3

Find the indicated term of the binomial expansion. $\left( 2 r - s ^ { 2 } \right) ^ { 9 }$; seventh

Accepted Answer

A)  $168 r ^ { 3 } s ^ { 6 }$ 
B)  $- 72 r ^ { 2 } s ^ { 7 }$ 
C)  $- 144 r ^ { 2 } s ^ { 14 }$ 
D)  $672 r ^ { 3 } s ^ { 12 }$ 
A)  $168 r ^ { 3 } s ^ { 6 }$ 
B)  $- 72 r ^ { 2 } s ^ { 7 }$ 
C)  $- 144 r ^ { 2 } s ^ { 14 }$ 
D)  $672 r ^ { 3 } s ^ { 12 }$

Question 4

Find the sum of the first 20 positive multiples of 4.

Accepted Answer

A)  840 
B)  800 
C)  36 
D)  40 
A)  840 
B)  800 
C)  36 
D)  40

Question 5

Rewrite the binomial of the form $( a - b ) ^ { n }$ as $[ a + ( - b ) ] ^ { n }$. Then expand the binomial. Use Pascal's triangle to find the coefficients.
$$\left( p ^ { 2 } - w \right) ^ { 3 }$$

Accepted Answer

A)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; p ^ { 6 } - 3 p ^ { 4 } w + 3 p ^ { 2 } w ^ { 2 } - w ^ { 3 }$ 
B)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; - p ^ { 6 } + w ^ { 3 }$ 
C)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; p ^ { 6 } - w ^ { 3 }$ 
D)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; - p ^ { 6 } + 3 p ^ { 4 } w - 3 p ^ { 2 } w ^ { 2 } + w ^ { 3 }$ 
A)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; p ^ { 6 } - 3 p ^ { 4 } w + 3 p ^ { 2 } w ^ { 2 } - w ^ { 3 }$ 
B)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; - p ^ { 6 } + w ^ { 3 }$ 
C)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; p ^ { 6 } - w ^ { 3 }$ 
D)  $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; - p ^ { 6 } + 3 p ^ { 4 } w - 3 p ^ { 2 } w ^ { 2 } + w ^ { 3 }$

Question 6

Find the seventh term of the arithmetic sequence given $$a _ { 1 } = - 8 \text { and } d = - 6$$

Accepted Answer

A)  -54 
B)  -44 
C)  -50 
D)  -62 
A)  -54 
B)  -44 
C)  -50 
D)  -62

Question 7

Determine the common ratio, r, for the geometric sequence. $12,3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \ldots$

Accepted Answer

A)  4 
B)  $\frac { 4 } { 3 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 3 } { 4 }$ 
A)  4 
B)  $\frac { 4 } { 3 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 3 } { 4 }$

Question 8

Write the nth term of the arithmetic sequence. 0, 3, 6, 9, 12

Accepted Answer

A)  $- 3 + 3 ^ { n }$ 
B)  $3 n$ 
C)  $3 ^ { n - 1 }$ 
D)  $- 3 + 3 n$ 
A)  $- 3 + 3 ^ { n }$ 
B)  $3 n$ 
C)  $3 ^ { n - 1 }$ 
D)  $- 3 + 3 n$

Question 9

Write the first five terms of the geometric sequence. a1 = -6, r = -1

Accepted Answer

A)  -1, -7, -13, -19, 11 
B)  -6, 6, -6, 6, -6 
C)  -1, 6, -36, 216, -1296 
D)  -6, -7, -8, 9, -10 
A)  -1, -7, -13, -19, 11 
B)  -6, 6, -6, 6, -6 
C)  -1, 6, -36, 216, -1296 
D)  -6, -7, -8, 9, -10

Question 10

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

Accepted Answer

A)  2 
B)  1 
C)  20 
D)  114 
A)  2 
B)  1 
C)  20 
D)  114

Question 11

Write the nth term of the arithmetic sequence. $1 , \frac { 7 } { 6 } , \frac { 4 } { 3 } , \frac { 3 } { 2 } , \frac { 5 } { 3 } , \ldots$

Accepted Answer

A)  $\frac { 5 } { 6 } + \frac { 1 } { 6 } n$ 
B)  $\frac { 1 } { 6 } + \frac { 5 } { 6 } n$ 
C)  $1 + \frac { 1 } { 6 } n$ 
D)  $1 + \frac { 5 } { 6 } n$ 
A)  $\frac { 5 } { 6 } + \frac { 1 } { 6 } n$ 
B)  $\frac { 1 } { 6 } + \frac { 5 } { 6 } n$ 
C)  $1 + \frac { 1 } { 6 } n$ 
D)  $1 + \frac { 5 } { 6 } n$

Question 12

Find the sum of the arithmetic series. -1 + (-6) + (-11) + ... + (-46)

Accepted Answer

A)  -210 
B)  -235 
C)  -230 
D)  -205 
A)  -210 
B)  -235 
C)  -230 
D)  -205

Question 13

Evaluate the expression. $$\frac { 6 ! } { 3 ! + 3 ! }$$

Accepted Answer

A)  6 
B)  20 
C)  23 
D)  1 
A)  6 
B)  20 
C)  23 
D)  1

Question 14

Find the number of terms, n, of the arithmetic sequence. -1, -9, -17, ..., -217

Accepted Answer

A)  30 
B)  28 
C)  27 
D)  29 
A)  30 
B)  28 
C)  27 
D)  29

Question 15

Determine the sum of the infinite series, if it exists. $$\frac { 2 } { 3 } + 1 + \frac { 3 } { 2 } + \frac { 9 } { 4 } + \ldots$$

Accepted Answer

A)  Sum does not exist 
B)  $\frac { 65 } { 12 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  $\frac { 4 } { 3 }$ 
A)  Sum does not exist 
B)  $\frac { 65 } { 12 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  $\frac { 4 } { 3 }$

Question 16

Find a formula for the nth term of the sequence. $1 , \frac { 1 } { 8 } , \frac { 1 } { 27 } , \frac { 1 } { 64 } , \ldots$

Accepted Answer

A)  $a ^ { n } = 3 ^ { n }$ 
B)  $a ^ { n } = \frac { 1 } { n ^ { 3 } }$ 
C)  $a ^ { n } = n ^ { 3 }$ 
D)  $a ^ { n } = \frac { 1 } { 3 ^ { n } }$ 
A)  $a ^ { n } = 3 ^ { n }$ 
B)  $a ^ { n } = \frac { 1 } { n ^ { 3 } }$ 
C)  $a ^ { n } = n ^ { 3 }$ 
D)  $a ^ { n } = \frac { 1 } { 3 ^ { n } }$

Question 17

Find the sum of the arithmetic series. $$\sum _ { i = 1 } ^ { 18 } ( - 5 i - 8 )$$

Accepted Answer

A)  $- 999$ 
B)  $- 53$ 
C)  $- 49$ 
D)  $- 882$ 
A)  $- 999$ 
B)  $- 53$ 
C)  $- 49$ 
D)  $- 882$

Question 18

Find the first three terms of the expansion. $$\left( p + q ^ { 2 } \right) ^ { 12 }$$

Accepted Answer

A)  $p ^ { 12 } + 12 p ^ { 11 } q + 66 p ^ { 10 } q ^ { 2 }$ 
B)  $p ^ { 12 } + 12 p ^ { 11 } q ^ { 2 } + 24 p ^ { 10 } q ^ { 4 }$ 
C)  $p ^ { 12 } + 12 p ^ { 11 } q + 24 p ^ { 10 } q ^ { 2 }$ 
D)  $p ^ { 12 } + 12 p ^ { 11 } q ^ { 2 } + 66 p ^ { 10 } q ^ { 4 }$ 
A)  $p ^ { 12 } + 12 p ^ { 11 } q + 66 p ^ { 10 } q ^ { 2 }$ 
B)  $p ^ { 12 } + 12 p ^ { 11 } q ^ { 2 } + 24 p ^ { 10 } q ^ { 4 }$ 
C)  $p ^ { 12 } + 12 p ^ { 11 } q + 24 p ^ { 10 } q ^ { 2 }$ 
D)  $p ^ { 12 } + 12 p ^ { 11 } q ^ { 2 } + 66 p ^ { 10 } q ^ { 4 }$

Question 19

Evaluate the expression.
6 !

Accepted Answer

A)  21 
B)  30 
C)  720 
D)  126 
A)  21 
B)  30 
C)  720 
D)  126

Question 20

The seating in a certain theater is arranged so that there are 44 seats in row 1, 45 seats in row 2, 46 seats in row 3, and so on. If there are 25 rows, what is the total revenue is the average ticket price is $8.00 per seat and the theater is sold out?

Accepted Answer

A)  $11,200.00 
B)  $272.00 
C)  $6800.00 
D)  $448.00 
A)  $11,200.00 
B)  $272.00 
C)  $6800.00 
D)  $448.00

Find the sum of the geometric series. $5 + 1 + \frac { 1 } { 5 } + \frac { 1 } { 25 } + \frac { 1 } { 125 }$

Find a formula for the nth term of the sequence. $\frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 } , \ldots$

Find the indicated term of the binomial expansion. $\left( 2 r - s ^ { 2 } \right) ^ { 9 }$ ; seventh

Find the sum of the first 20 positive multiples of 4.

Rewrite the binomial of the form $( a - b ) ^ { n }$ as $[ a + ( - b ) ] ^ { n }$ . Then expand the binomial. Use Pascal's triangle to find the coefficients. $\left( p ^ { 2 } - w \right) ^ { 3 }$

Find the seventh term of the arithmetic sequence given $a _ { 1 } = - 8 \text { and } d = - 6$

Determine the common ratio, r, for the geometric sequence. $12,3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \ldots$

Write the nth term of the arithmetic sequence. 0, 3, 6, 9, 12

Write the first five terms of the geometric sequence. a₁ = -6, r = -1

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

Write the nth term of the arithmetic sequence. $1 , \frac { 7 } { 6 } , \frac { 4 } { 3 } , \frac { 3 } { 2 } , \frac { 5 } { 3 } , \ldots$

Find the sum of the arithmetic series. -1 + (-6) + (-11) + ... + (-46)

Evaluate the expression. $\frac { 6 ! } { 3 ! + 3 ! }$

Find the number of terms, n, of the arithmetic sequence. -1, -9, -17, ..., -217

Determine the sum of the infinite series, if it exists. $\frac { 2 } { 3 } + 1 + \frac { 3 } { 2 } + \frac { 9 } { 4 } + \ldots$

Find a formula for the nth term of the sequence. $1 , \frac { 1 } { 8 } , \frac { 1 } { 27 } , \frac { 1 } { 64 } , \ldots$

Find the sum of the arithmetic series. $\sum _ { i = 1 } ^ { 18 } ( - 5 i - 8 )$

Find the first three terms of the expansion. $\left( p + q ^ { 2 } \right) ^ { 12 }$

Evaluate the expression. 6 !

The seating in a certain theater is arranged so that there are 44 seats in row 1, 45 seats in row 2, 46 seats in row 3, and so on. If there are 25 rows, what is the total revenue is the average ticket price is $8.00 per seat and the theater is sold out?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Exam 10: Binomial Expansions, Sequences, and Series

Find the sum of the geometric series. 5+1+15+125+11255 + 1 + \frac { 1 } { 5 } + \frac { 1 } { 25 } + \frac { 1 } { 125 }5+1+51​+251​+1251​

Find a formula for the nth term of the sequence. 15,125,1125,1625,…\frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 } , \ldots51​,251​,1251​,6251​,…

Find the indicated term of the binomial expansion. (2r−s2)9\left( 2 r - s ^ { 2 } \right) ^ { 9 }(2r−s2)9 ; seventh

Find the sum of the first 20 positive multiples of 4.

Rewrite the binomial of the form (a−b)n( a - b ) ^ { n }(a−b)n as [a+(−b)]n[ a + ( - b ) ] ^ { n }[a+(−b)]n . Then expand the binomial. Use Pascal's triangle to find the coefficients. (p2−w)3\left( p ^ { 2 } - w \right) ^ { 3 }(p2−w)3

Find the seventh term of the arithmetic sequence given a1=−8 and d=−6a _ { 1 } = - 8 \text { and } d = - 6a1​=−8 and d=−6

Determine the common ratio, r, for the geometric sequence. 12,3,34,316,…12,3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \ldots12,3,43​,163​,…

Write the nth term of the arithmetic sequence. 0, 3, 6, 9, 12

Write the first five terms of the geometric sequence. a1 = -6, r = -1

Evaluate the expression. 5!3!\frac { 5 ! } { 3 ! }3!5!​

Write the nth term of the arithmetic sequence. 1,76,43,32,53,…1 , \frac { 7 } { 6 } , \frac { 4 } { 3 } , \frac { 3 } { 2 } , \frac { 5 } { 3 } , \ldots1,67​,34​,23​,35​,…

Find the sum of the arithmetic series. -1 + (-6) + (-11) + ... + (-46)

Evaluate the expression. 6!3!+3!\frac { 6 ! } { 3 ! + 3 ! }3!+3!6!​

Find the number of terms, n, of the arithmetic sequence. -1, -9, -17, ..., -217

Determine the sum of the infinite series, if it exists. 23+1+32+94+…\frac { 2 } { 3 } + 1 + \frac { 3 } { 2 } + \frac { 9 } { 4 } + \ldots32​+1+23​+49​+…

Find a formula for the nth term of the sequence. 1,18,127,164,…1 , \frac { 1 } { 8 } , \frac { 1 } { 27 } , \frac { 1 } { 64 } , \ldots1,81​,271​,641​,…

Find the sum of the arithmetic series. ∑i=118(−5i−8)\sum _ { i = 1 } ^ { 18 } ( - 5 i - 8 )∑i=118​(−5i−8)

Find the first three terms of the expansion. (p+q2)12\left( p + q ^ { 2 } \right) ^ { 12 }(p+q2)12

Evaluate the expression. 6 !

The seating in a certain theater is arranged so that there are 44 seats in row 1, 45 seats in row 2, 46 seats in row 3, and so on. If there are 25 rows, what is the total revenue is the average ticket price is $8.00 per seat and the theater is sold out?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Find the sum of the geometric series. $5 + 1 + \frac { 1 } { 5 } + \frac { 1 } { 25 } + \frac { 1 } { 125 }$

Find a formula for the nth term of the sequence. $\frac { 1 } { 5 } , \frac { 1 } { 25 } , \frac { 1 } { 125 } , \frac { 1 } { 625 } , \ldots$

Find the indicated term of the binomial expansion. $\left( 2 r - s ^ { 2 } \right) ^ { 9 }$ ; seventh

Rewrite the binomial of the form $( a - b ) ^ { n }$ as $[ a + ( - b ) ] ^ { n }$ . Then expand the binomial. Use Pascal's triangle to find the coefficients. $\left( p ^ { 2 } - w \right) ^ { 3 }$

Find the seventh term of the arithmetic sequence given $a _ { 1 } = - 8 \text { and } d = - 6$

Determine the common ratio, r, for the geometric sequence. $12,3 , \frac { 3 } { 4 } , \frac { 3 } { 16 } , \ldots$

Write the first five terms of the geometric sequence. a₁ = -6, r = -1

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

Write the nth term of the arithmetic sequence. $1 , \frac { 7 } { 6 } , \frac { 4 } { 3 } , \frac { 3 } { 2 } , \frac { 5 } { 3 } , \ldots$

Evaluate the expression. $\frac { 6 ! } { 3 ! + 3 ! }$

Determine the sum of the infinite series, if it exists. $\frac { 2 } { 3 } + 1 + \frac { 3 } { 2 } + \frac { 9 } { 4 } + \ldots$

Find a formula for the nth term of the sequence. $1 , \frac { 1 } { 8 } , \frac { 1 } { 27 } , \frac { 1 } { 64 } , \ldots$

Find the sum of the arithmetic series. $\sum _ { i = 1 } ^ { 18 } ( - 5 i - 8 )$

Find the first three terms of the expansion. $\left( p + q ^ { 2 } \right) ^ { 12 }$