Question 1

Determine whether the sequence $\ln 7 , \ln 14 , \ln 21 , \ln 28 , \ldots$ is arithmetic. If so, find the common difference.

Accepted Answer

A) arithmetic; 14 
B) arithmetic; 2 
C) arithmetic;7 
D) arithmetic; 28 
E) not arithmetic 
A) arithmetic; 14 
B) arithmetic; 2 
C) arithmetic;7 
D) arithmetic; 28 
E) not arithmetic E

Question 2

Find the $6$ th term in the expansion of $( 2 x + y ) ^ { 8 }$ .

Accepted Answer

A)  $28 x ^ { 3 } y ^ { 6 }$ 
B)  $224 x ^ { 2 } y ^ { 6 }$ 
C)  $28 x ^ { 2 } y ^ { 6 }$ 
D)  $448 x ^ { 3 } y ^ { 5 }$ 
E)  $112 x ^ { 3 } y ^ { 5 }$ 
A)  $28 x ^ { 3 } y ^ { 6 }$ 
B)  $224 x ^ { 2 } y ^ { 6 }$ 
C)  $28 x ^ { 2 } y ^ { 6 }$ 
D)  $448 x ^ { 3 } y ^ { 5 }$ 
E)  $112 x ^ { 3 } y ^ { 5 }$ D

Question 3

Write the first five terms of the sequence $a _ { n } = \frac { n } { 9 n + 1 }$ . Assume that n begins with 1.

Accepted Answer

A)  $a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = - \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = - \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 }$ 
B)  $a _ { 1 } = \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = \frac { 5 } { 46 }$ 
C)  $a _ { 1 } = 0 , a _ { 2 } = - \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = - \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 }$ 
D)  $a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 }$ 
E)  $a _ { 1 } = 0 , a _ { 2 } = \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 }$ 
A)  $a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = - \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = - \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 }$ 
B)  $a _ { 1 } = \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = \frac { 5 } { 46 }$ 
C)  $a _ { 1 } = 0 , a _ { 2 } = - \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = - \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 }$ 
D)  $a _ { 1 } = - \frac { 1 } { 10 } , a _ { 2 } = \frac { 2 } { 19 } , a _ { 3 } = - \frac { 3 } { 28 } , a _ { 4 } = \frac { 4 } { 37 } , a _ { 5 } = - \frac { 5 } { 46 }$ 
E)  $a _ { 1 } = 0 , a _ { 2 } = \frac { 1 } { 10 } , a _ { 3 } = \frac { 2 } { 19 } , a _ { 4 } = \frac { 3 } { 28 } , a _ { 5 } = \frac { 4 } { 37 }$ B

Question 4

In section 112 of Hammer Stadium there are $25$ rows of seats: $16$ in the first row, $17$ seats in the second row, $18$ seats in the third row, and so on. What is the cost of each ticket if the total cost of all the seats in section 112 is $\$ 29,400$ ? Round the answer to two decimal places.

Accepted Answer

A)  $\$ 42.00$ 
B)  $\$ 43.25$ 
C)  $\$ 48.75$ 
D)  $\$ 45.75$ 
E)  $\$ 39.50$ 
A)  $\$ 42.00$ 
B)  $\$ 43.25$ 
C)  $\$ 48.75$ 
D)  $\$ 45.75$ 
E)  $\$ 39.50$

Question 5

Write the first five terms of the geometric sequence, given $a_{1}=-9$ and $r=-\frac{1}{3}$ .

Accepted Answer

A)  $-9,3,-1, \frac{1}{3},-\frac{1}{9}$ 
B)  $-9,-3,1,-\frac{1}{3},-\frac{1}{9}$ 
C)  $-9,27,-1, \frac{1}{9},-\frac{1}{27}$ 
D)  $-27,9,1, \frac{1}{9},-\frac{1}{27}$ 
E)  $- 27,9 , - 1 , - \frac { 1 } { 3 } , - \frac { 1 } { 27 }$ 
A)  $-9,3,-1, \frac{1}{3},-\frac{1}{9}$ 
B)  $-9,-3,1,-\frac{1}{3},-\frac{1}{9}$ 
C)  $-9,27,-1, \frac{1}{9},-\frac{1}{27}$ 
D)  $-27,9,1, \frac{1}{9},-\frac{1}{27}$ 
E)  $- 27,9 , - 1 , - \frac { 1 } { 3 } , - \frac { 1 } { 27 }$

Question 6

Write the first five terms of the sequence $( - 1 ) ^ { n } 9 n$ . Assume that n begins with 1.

Accepted Answer

A)  $a _ { 1 } = 0 , a _ { 2 } = - 9 , a _ { 3 } = 18 , a _ { 4 } = - 27 , a _ { 5 } = 36$ 
B)  $a _ { 1 } = 9 , a _ { 2 } = 18 , a _ { 3 } = 27 , a _ { 4 } = 36 , a _ { 5 } = 45$ 
C)  $a _ { 1 } = 0 , a _ { 2 } = - 18 , a _ { 3 } = 27 , a _ { 4 } = - 36 , a _ { 5 } = 45$ 
D)  $a _ { 1 } = - 9 , a _ { 2 } = 18 , a _ { 3 } = - 27 , a _ { 4 } = 36 , a _ { 5 } = - 45$ 
E)  $a _ { 1 } = 9 , a _ { 2 } = - 18 , a _ { 3 } = 27 , a _ { 4 } = - 36 , a _ { 5 } = 45$ 
A)  $a _ { 1 } = 0 , a _ { 2 } = - 9 , a _ { 3 } = 18 , a _ { 4 } = - 27 , a _ { 5 } = 36$ 
B)  $a _ { 1 } = 9 , a _ { 2 } = 18 , a _ { 3 } = 27 , a _ { 4 } = 36 , a _ { 5 } = 45$ 
C)  $a _ { 1 } = 0 , a _ { 2 } = - 18 , a _ { 3 } = 27 , a _ { 4 } = - 36 , a _ { 5 } = 45$ 
D)  $a _ { 1 } = - 9 , a _ { 2 } = 18 , a _ { 3 } = - 27 , a _ { 4 } = 36 , a _ { 5 } = - 45$ 
E)  $a _ { 1 } = 9 , a _ { 2 } = - 18 , a _ { 3 } = 27 , a _ { 4 } = - 36 , a _ { 5 } = 45$

Question 7

Use the Binomial Theorem to expand the expression $( x + 3 y ) ^ { 4 }$ .

Accepted Answer

A)  $x ^ { 4 } + 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } + 108 x y ^ { 3 } + 81 y ^ { 4 }$ 
B)  $x ^ { 4 } + 3 x ^ { 3 } y + 9 x ^ { 2 } y ^ { 2 } + 27 x y ^ { 3 } + 81 y ^ { 4 }$ 
C)  $x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }$ 
D)  $x ^ { 4 } + 81 y ^ { 4 }$ 
E)  $x ^ { 4 } + 15 x ^ { 3 } y + 90 x ^ { 2 } y ^ { 2 } + 135 x y ^ { 3 } + 81 y ^ { 4 }$ 
A)  $x ^ { 4 } + 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } + 108 x y ^ { 3 } + 81 y ^ { 4 }$ 
B)  $x ^ { 4 } + 3 x ^ { 3 } y + 9 x ^ { 2 } y ^ { 2 } + 27 x y ^ { 3 } + 81 y ^ { 4 }$ 
C)  $x ^ { 4 } + 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + y ^ { 4 }$ 
D)  $x ^ { 4 } + 81 y ^ { 4 }$ 
E)  $x ^ { 4 } + 15 x ^ { 3 } y + 90 x ^ { 2 } y ^ { 2 } + 135 x y ^ { 3 } + 81 y ^ { 4 }$

Question 8

Use the Binomial Theorem to expand the expression $( 5 a + 4 b ) ^ { 4 }$ .

Accepted Answer

A)  $625 a ^ { 4 } + 256 b ^ { 4 }$ 
B)  $a ^ { 4 } + 4 a ^ { 3 } b + 6 a ^ { 2 } b ^ { 2 } + 4 a b ^ { 3 } + b ^ { 4 }$ 
C)  $625 a ^ { 4 } + 500 a ^ { 3 } b + 400 a ^ { 2 } b ^ { 2 } + 320 a b ^ { 3 } + 256 b ^ { 4 }$ 
D)  $a ^ { 4 } + 16 a ^ { 3 } b + 96 a ^ { 2 } b ^ { 2 } + 256 a b ^ { 3 } + 256 b ^ { 4 }$ 
E)  $625 a ^ { 4 } + 2000 a ^ { 3 } b + 2400 a ^ { 2 } b ^ { 2 } + 1280 a b ^ { 3 } + 256 b ^ { 4 }$ 
A)  $625 a ^ { 4 } + 256 b ^ { 4 }$ 
B)  $a ^ { 4 } + 4 a ^ { 3 } b + 6 a ^ { 2 } b ^ { 2 } + 4 a b ^ { 3 } + b ^ { 4 }$ 
C)  $625 a ^ { 4 } + 500 a ^ { 3 } b + 400 a ^ { 2 } b ^ { 2 } + 320 a b ^ { 3 } + 256 b ^ { 4 }$ 
D)  $a ^ { 4 } + 16 a ^ { 3 } b + 96 a ^ { 2 } b ^ { 2 } + 256 a b ^ { 3 } + 256 b ^ { 4 }$ 
E)  $625 a ^ { 4 } + 2000 a ^ { 3 } b + 2400 a ^ { 2 } b ^ { 2 } + 1280 a b ^ { 3 } + 256 b ^ { 4 }$

Question 9

Write an expression for the n th term of the sequence $\frac { 8 } { 9 } , \frac { 9 } { 10 } , \frac { 10 } { 11 } , \frac { 11 } { 12 } , \frac { 12 } { 13 } ,....$ Assume that n begins with 1.

Accepted Answer

A)  $a _ { n } = \frac { n + 7 } { n + 8 }$ 
B)  $a _ { n } = \frac { n + 8 } { n + 9 }$ 
C)  $a _ { n } = \frac { ( n + 8 ) ! } { ( n + 9 ) ! }$ 
D)  $a _ { n } = \frac { n + 9 } { n + 10 }$ 
E)  $a _ { n } = \frac { ( n + 7 ) ! } { ( n + 8 ) ! }$ 
A)  $a _ { n } = \frac { n + 7 } { n + 8 }$ 
B)  $a _ { n } = \frac { n + 8 } { n + 9 }$ 
C)  $a _ { n } = \frac { ( n + 8 ) ! } { ( n + 9 ) ! }$ 
D)  $a _ { n } = \frac { n + 9 } { n + 10 }$ 
E)  $a _ { n } = \frac { ( n + 7 ) ! } { ( n + 8 ) ! }$

Question 10

Find the $6$ th term in the expansion of $( x + y ) ^ { 9 }$ .

Accepted Answer

A)  $84 x ^ { 4 } y ^ { 5 }$ 
B)  $84 x ^ { 3 } y ^ { 6 }$ 
C)  $84 x ^ { 4 } y ^ { 6 }$ 
D)  $126 x ^ { 4 } y ^ { 5 }$ 
E)  $126 x ^ { 3 } y ^ { 6 }$ 
A)  $84 x ^ { 4 } y ^ { 5 }$ 
B)  $84 x ^ { 3 } y ^ { 6 }$ 
C)  $84 x ^ { 4 } y ^ { 6 }$ 
D)  $126 x ^ { 4 } y ^ { 5 }$ 
E)  $126 x ^ { 3 } y ^ { 6 }$

Question 11

A museum only allows patrons to enter at fifteen minute intervals. An observer notices that every weekday at 2:00 there are $8$ people waiting at the entrance and at 3:00 there are $20$ people waiting. In addition, there are $10$ people waiting at the entrance at all 15-minute intervals that are not on the hour. This pattern continues through 6:00. How many people wait to enter the museum in the interval from 2:00 to 6:00?

Accepted Answer

A)  $280$ 
B)  $232$ 
C)  $291$ 
D)  $248$ 
E)  $208$ 
A)  $280$ 
B)  $232$ 
C)  $291$ 
D)  $248$ 
E)  $208$

Question 12

Write the first five terms of the sequence $a _ { n } = \frac { - 3 + \left( - 5 ^ { n } \right) } { n ! }$ . Assume that n begins with 1.

Accepted Answer

A)  $a _ { 1 } = - 2 , a _ { 2 } = 14 , a _ { 3 } = - \frac { 61 } { 3 } , a _ { 4 } = \frac { 157 } { 6 } , a _ { 5 } = - \frac { 1561 } { 60 }$ 
B)  $a _ { 1 } = 8 , a _ { 2 } = - 11 , a _ { 3 } = \frac { 64 } { 3 } , a _ { 4 } = - \frac { 311 } { 12 } , a _ { 5 } = \frac { 391 } { 15 }$ 
C)  $a _ { 1 } = - 2 , a _ { 2 } = 14 , a _ { 3 } = \frac { 61 } { 3 } , a _ { 4 } = - \frac { 311 } { 6 } , a _ { 5 } = - \frac { 391 } { 15 }$ 
D)  $a _ { 1 } = 2 , a _ { 2 } = - 14 , a _ { 3 } = \frac { 61 } { 3 } , a _ { 4 } = - \frac { 157 } { 6 } , a _ { 5 } = \frac { 1561 } { 60 }$ 
E)  $a _ { 1 } = - 8 , a _ { 2 } = 11 , a _ { 3 } = - \frac { 64 } { 3 } , a _ { 4 } = \frac { 311 } { 12 } , a _ { 5 } = - \frac { 391 } { 15 }$ 
A)  $a _ { 1 } = - 2 , a _ { 2 } = 14 , a _ { 3 } = - \frac { 61 } { 3 } , a _ { 4 } = \frac { 157 } { 6 } , a _ { 5 } = - \frac { 1561 } { 60 }$ 
B)  $a _ { 1 } = 8 , a _ { 2 } = - 11 , a _ { 3 } = \frac { 64 } { 3 } , a _ { 4 } = - \frac { 311 } { 12 } , a _ { 5 } = \frac { 391 } { 15 }$ 
C)  $a _ { 1 } = - 2 , a _ { 2 } = 14 , a _ { 3 } = \frac { 61 } { 3 } , a _ { 4 } = - \frac { 311 } { 6 } , a _ { 5 } = - \frac { 391 } { 15 }$ 
D)  $a _ { 1 } = 2 , a _ { 2 } = - 14 , a _ { 3 } = \frac { 61 } { 3 } , a _ { 4 } = - \frac { 157 } { 6 } , a _ { 5 } = \frac { 1561 } { 60 }$ 
E)  $a _ { 1 } = - 8 , a _ { 2 } = 11 , a _ { 3 } = - \frac { 64 } { 3 } , a _ { 4 } = \frac { 311 } { 12 } , a _ { 5 } = - \frac { 391 } { 15 }$

Question 13

Simplify the expression $\frac { 8 ! } { 11 ! }$ .

Accepted Answer

A)  $\frac { 1 } { 729 }$ 
B)  $\frac { 1 } { 990 }$ 
C)  $\frac { 1 } { 720 }$ 
D)  990 
E)  720 
A)  $\frac { 1 } { 729 }$ 
B)  $\frac { 1 } { 990 }$ 
C)  $\frac { 1 } { 720 }$ 
D)  990 
E)  720

Question 14

Evaluate the binomial coefficient $${ } _ { 15 } C _ { 13 }$$ .

Accepted Answer

A)  $120$ 
B)  $300$ 
C)  $118$ 
D)  $317$ 
E)  $105$ 
A)  $120$ 
B)  $300$ 
C)  $118$ 
D)  $317$ 
E)  $105$

Question 15

Use Pascal s Triangle to expand the expression $( 3 y + z ) ^ { 6 }$ .

Accepted Answer

A)  $729 y ^ { 6 } + z ^ { 6 }$ 
B)  $729 y ^ { 6 } + 243 y ^ { 5 } z + 81 y ^ { 4 } z ^ { 2 } + 27 y ^ { 3 } z ^ { 3 } + 9 y ^ { 2 } z ^ { 4 } + 3 y z ^ { 5 } + z ^ { 6 }$ 
C)  $y ^ { 6 } + y ^ { 5 } z + y ^ { 4 } z ^ { 2 } + y ^ { 3 } z ^ { 3 } + y ^ { 2 } z ^ { 4 } + y z ^ { 5 } + z ^ { 6 }$ 
D)  $729 y ^ { 6 } + 1458 y ^ { 5 } z + 1215 y ^ { 4 } z ^ { 2 } + 540 y ^ { 3 } z ^ { 3 } + 135 y ^ { 2 } z ^ { 4 } + 18 y z ^ { 5 } + z ^ { 6 }$ 
E)  $3 y ^ { 6 } + z ^ { 6 }$ 
A)  $729 y ^ { 6 } + z ^ { 6 }$ 
B)  $729 y ^ { 6 } + 243 y ^ { 5 } z + 81 y ^ { 4 } z ^ { 2 } + 27 y ^ { 3 } z ^ { 3 } + 9 y ^ { 2 } z ^ { 4 } + 3 y z ^ { 5 } + z ^ { 6 }$ 
C)  $y ^ { 6 } + y ^ { 5 } z + y ^ { 4 } z ^ { 2 } + y ^ { 3 } z ^ { 3 } + y ^ { 2 } z ^ { 4 } + y z ^ { 5 } + z ^ { 6 }$ 
D)  $729 y ^ { 6 } + 1458 y ^ { 5 } z + 1215 y ^ { 4 } z ^ { 2 } + 540 y ^ { 3 } z ^ { 3 } + 135 y ^ { 2 } z ^ { 4 } + 18 y z ^ { 5 } + z ^ { 6 }$ 
E)  $3 y ^ { 6 } + z ^ { 6 }$

Question 16

Write the sum using sigma notation. Begin with $k = 0$ . $\frac { 1 } { 9 ^ { 0 } } - \frac { 1 } { 9 ^ { 1 } } + \frac { 1 } { 9 ^ { 2 } } - \frac { 1 } { 9 ^ { 3 } } + \ldots - \frac { 1 } { 9 ^ { 11 } }$

Accepted Answer

A)  $\sum _ { k = 0 } ^ { 10 } - \frac { 1 } { 9 ^ { k } }$ 
B)  $\sum _ { k = 0 } ^ { 11 } \left( - \frac { 1 } { 9 } \right) ^ { k + 1 }$ 
C)  $\sum _ { k = 0 } ^ { 10 } \left( - \frac { 1 } { 9 } \right) ^ { k + 1 }$ 
D)  $\sum _ { k = 0 } ^ { 11 } - \frac { 1 } { 9 ^ { k } }$ 
E)  $\sum _ { k = 0 } ^ { 11 } \left( - \frac { 1 } { 9 } \right) ^ { k }$ 
A)  $\sum _ { k = 0 } ^ { 10 } - \frac { 1 } { 9 ^ { k } }$ 
B)  $\sum _ { k = 0 } ^ { 11 } \left( - \frac { 1 } { 9 } \right) ^ { k + 1 }$ 
C)  $\sum _ { k = 0 } ^ { 10 } \left( - \frac { 1 } { 9 } \right) ^ { k + 1 }$ 
D)  $\sum _ { k = 0 } ^ { 11 } - \frac { 1 } { 9 ^ { k } }$ 
E)  $\sum _ { k = 0 } ^ { 11 } \left( - \frac { 1 } { 9 } \right) ^ { k }$

Question 17

Find the coefficient of the term containing $x ^ { 7 }$ in the expansion of the binomial $( x + 4 ) ^ { 9 }$ .

Accepted Answer

A)  $576$ 
B)  $130$ 
C)  $2,304$ 
D)  $7,344$ 
E)  $144$ 
A)  $576$ 
B)  $130$ 
C)  $2,304$ 
D)  $7,344$ 
E)  $144$

Question 18

Evaluate the binomial coefficient $${ } _ { 7 } C _ { 3 }$$ .

Accepted Answer

A)  $6$ 
B)  $5,034$ 
C)  $840$ 
D)  $35$ 
E)  $210$ 
A)  $6$ 
B)  $5,034$ 
C)  $840$ 
D)  $35$ 
E)  $210$

Question 19

Find the n th partial sum of the geometric sequence. $1,-4,16,-64,256, \ldots, \quad n=7$

Accepted Answer

A) 3326 
B) 3277 
C) -819 
D) 3620 
E) -51 
A) 3326 
B) 3277 
C) -819 
D) 3620 
E) -51

Question 20

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $a_{1}=10, a_{2}=2$

Accepted Answer

A)  $a_{n}=10\left(\frac{1}{5}\right)^{n-1}$ 
B)  $a_{n}=2^{n-1}$ 
C)  $a_{n}=2(5)^{n-1}$ 
D)  $a_{n}=2(5)^{n}$ 
E)  $a_{n}=10\left(\frac{1}{5}\right)^{x}$ 
A)  $a_{n}=10\left(\frac{1}{5}\right)^{n-1}$ 
B)  $a_{n}=2^{n-1}$ 
C)  $a_{n}=2(5)^{n-1}$ 
D)  $a_{n}=2(5)^{n}$ 
E)  $a_{n}=10\left(\frac{1}{5}\right)^{x}$

Determine whether the sequence $\ln 7 , \ln 14 , \ln 21 , \ln 28 , \ldots$ is arithmetic. If so, find the common difference.

Find the $6$ th term in the expansion of $( 2 x + y ) ^ { 8 }$ .

Write the first five terms of the sequence $a _ { n } = \frac { n } { 9 n + 1 }$ . Assume that n begins with 1.

In section 112 of Hammer Stadium there are $25$ rows of seats: $16$ in the first row, $17$ seats in the second row, $18$ seats in the third row, and so on. What is the cost of each ticket if the total cost of all the seats in section 112 is $\$ 29,400$ ? Round the answer to two decimal places.

Write the first five terms of the geometric sequence, given $a_{1}=-9$ and $r=-\frac{1}{3}$ .

Write the first five terms of the sequence $( - 1 ) ^ { n } 9 n$ . Assume that n begins with 1.

Use the Binomial Theorem to expand the expression $( x + 3 y ) ^ { 4 }$ .

Use the Binomial Theorem to expand the expression $( 5 a + 4 b ) ^ { 4 }$ .

Write an expression for the n th term of the sequence $\frac { 8 } { 9 } , \frac { 9 } { 10 } , \frac { 10 } { 11 } , \frac { 11 } { 12 } , \frac { 12 } { 13 } ,....$ Assume that n begins with 1.

Find the $6$ th term in the expansion of $( x + y ) ^ { 9 }$ .

Write the first five terms of the sequence $a _ { n } = \frac { - 3 + \left( - 5 ^ { n } \right) } { n ! }$ . Assume that n begins with 1.

Simplify the expression $\frac { 8 ! } { 11 ! }$ .

Evaluate the binomial coefficient ${ } _ { 15 } C _ { 13 }$ .

Use Pascal s Triangle to expand the expression $( 3 y + z ) ^ { 6 }$ .

Write the sum using sigma notation. Begin with $k = 0$ . $\frac { 1 } { 9 ^ { 0 } } - \frac { 1 } { 9 ^ { 1 } } + \frac { 1 } { 9 ^ { 2 } } - \frac { 1 } { 9 ^ { 3 } } + \ldots - \frac { 1 } { 9 ^ { 11 } }$

Find the coefficient of the term containing $x ^ { 7 }$ in the expansion of the binomial $( x + 4 ) ^ { 9 }$ .

Evaluate the binomial coefficient ${ } _ { 7 } C _ { 3 }$ .

Find the n th partial sum of the geometric sequence. $1,-4,16,-64,256, \ldots, \quad n=7$

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $a_{1}=10, a_{2}=2$

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

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Rational Expressions, Equations, and Functions

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Exam 11: Sequences, Series, and the Binomial Theorem

Determine whether the sequence ln⁡7,ln⁡14,ln⁡21,ln⁡28,…\ln 7 , \ln 14 , \ln 21 , \ln 28 , \ldotsln7,ln14,ln21,ln28,… is arithmetic. If so, find the common difference.

Find the 666 th term in the expansion of (2x+y)8( 2 x + y ) ^ { 8 }(2x+y)8 .

Write the first five terms of the sequence an=n9n+1a _ { n } = \frac { n } { 9 n + 1 }an​=9n+1n​ . Assume that n begins with 1.

Write the first five terms of the geometric sequence, given a1=−9a_{1}=-9a1​=−9 and r=−13r=-\frac{1}{3}r=−31​ .

Write the first five terms of the sequence (−1)n9n( - 1 ) ^ { n } 9 n(−1)n9n . Assume that n begins with 1.

Use the Binomial Theorem to expand the expression (x+3y)4( x + 3 y ) ^ { 4 }(x+3y)4 .

Use the Binomial Theorem to expand the expression (5a+4b)4( 5 a + 4 b ) ^ { 4 }(5a+4b)4 .

Write an expression for the n th term of the sequence 89,910,1011,1112,1213,....\frac { 8 } { 9 } , \frac { 9 } { 10 } , \frac { 10 } { 11 } , \frac { 11 } { 12 } , \frac { 12 } { 13 } ,....98​,109​,1110​,1211​,1312​,.... Assume that n begins with 1.

Find the 666 th term in the expansion of (x+y)9( x + y ) ^ { 9 }(x+y)9 .

Write the first five terms of the sequence an=−3+(−5n)n!a _ { n } = \frac { - 3 + \left( - 5 ^ { n } \right) } { n ! }an​=n!−3+(−5n)​ . Assume that n begins with 1.

Simplify the expression 8!11!\frac { 8 ! } { 11 ! }11!8!​ .

Evaluate the binomial coefficient 15C13{ } _ { 15 } C _ { 13 }15​C13​ .

Use Pascal s Triangle to expand the expression (3y+z)6( 3 y + z ) ^ { 6 }(3y+z)6 .

Write the sum using sigma notation. Begin with k=0k = 0k=0 . 190−191+192−193+…−1911\frac { 1 } { 9 ^ { 0 } } - \frac { 1 } { 9 ^ { 1 } } + \frac { 1 } { 9 ^ { 2 } } - \frac { 1 } { 9 ^ { 3 } } + \ldots - \frac { 1 } { 9 ^ { 11 } }901​−911​+921​−931​+…−9111​

Find the coefficient of the term containing x7x ^ { 7 }x7 in the expansion of the binomial (x+4)9( x + 4 ) ^ { 9 }(x+4)9 .

Evaluate the binomial coefficient 7C3{ } _ { 7 } C _ { 3 }7​C3​ .

Find the n th partial sum of the geometric sequence. 1,−4,16,−64,256,…,n=71,-4,16,-64,256, \ldots, \quad n=71,−4,16,−64,256,…,n=7

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. a1=10,a2=2a_{1}=10, a_{2}=2a1​=10,a2​=2

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Filters

Determine whether the sequence $\ln 7 , \ln 14 , \ln 21 , \ln 28 , \ldots$ is arithmetic. If so, find the common difference.

Find the $6$ th term in the expansion of $( 2 x + y ) ^ { 8 }$ .

Write the first five terms of the sequence $a _ { n } = \frac { n } { 9 n + 1 }$ . Assume that n begins with 1.

Write the first five terms of the geometric sequence, given $a_{1}=-9$ and $r=-\frac{1}{3}$ .

Write the first five terms of the sequence $( - 1 ) ^ { n } 9 n$ . Assume that n begins with 1.

Use the Binomial Theorem to expand the expression $( x + 3 y ) ^ { 4 }$ .

Use the Binomial Theorem to expand the expression $( 5 a + 4 b ) ^ { 4 }$ .

Write an expression for the n th term of the sequence $\frac { 8 } { 9 } , \frac { 9 } { 10 } , \frac { 10 } { 11 } , \frac { 11 } { 12 } , \frac { 12 } { 13 } ,....$ Assume that n begins with 1.

Find the $6$ th term in the expansion of $( x + y ) ^ { 9 }$ .

Write the first five terms of the sequence $a _ { n } = \frac { - 3 + \left( - 5 ^ { n } \right) } { n ! }$ . Assume that n begins with 1.

Simplify the expression $\frac { 8 ! } { 11 ! }$ .

Evaluate the binomial coefficient ${ } _ { 15 } C _ { 13 }$ .

Use Pascal s Triangle to expand the expression $( 3 y + z ) ^ { 6 }$ .

Write the sum using sigma notation. Begin with $k = 0$ . $\frac { 1 } { 9 ^ { 0 } } - \frac { 1 } { 9 ^ { 1 } } + \frac { 1 } { 9 ^ { 2 } } - \frac { 1 } { 9 ^ { 3 } } + \ldots - \frac { 1 } { 9 ^ { 11 } }$

Find the coefficient of the term containing $x ^ { 7 }$ in the expansion of the binomial $( x + 4 ) ^ { 9 }$ .

Evaluate the binomial coefficient ${ } _ { 7 } C _ { 3 }$ .

Find the n th partial sum of the geometric sequence. $1,-4,16,-64,256, \ldots, \quad n=7$

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $a_{1}=10, a_{2}=2$