Question 1

Use the Binomial Theorem to expand the expression $( u - 2 v ) ^ { 3 }$ .

Accepted Answer

A)  $u ^ { 3 } - u ^ { 2 } v + u v ^ { 2 } - v ^ { 3 }$ 
B)  $u ^ { 3 } + 6 u ^ { 2 } v - 6 u v ^ { 2 } + 2 v ^ { 3 }$ 
C)  $u ^ { 3 } - 8 v ^ { 3 }$ 
D)  $u ^ { 3 } - 6 u ^ { 2 } v + 6 u v ^ { 2 } - 2 v ^ { 3 }$ 
E)  $u ^ { 3 } - 6 u ^ { 2 } v + 12 u v ^ { 2 } - 8 v ^ { 3 }$ 
A)  $u ^ { 3 } - u ^ { 2 } v + u v ^ { 2 } - v ^ { 3 }$ 
B)  $u ^ { 3 } + 6 u ^ { 2 } v - 6 u v ^ { 2 } + 2 v ^ { 3 }$ 
C)  $u ^ { 3 } - 8 v ^ { 3 }$ 
D)  $u ^ { 3 } - 6 u ^ { 2 } v + 6 u v ^ { 2 } - 2 v ^ { 3 }$ 
E)  $u ^ { 3 } - 6 u ^ { 2 } v + 12 u v ^ { 2 } - 8 v ^ { 3 }$

Question 2

Find a formula for the n th term of the arithmetic sequence. $a _ { 5 } = 22 , a _ { 6 } = 29$

Accepted Answer

A)  $7 n - 13$ 
B)  $7 n - 20$ 
C)  $7 n + 15$ 
D)  $7 n + 29$ 
E)  $7 n - 6$ 
A)  $7 n - 13$ 
B)  $7 n - 20$ 
C)  $7 n + 15$ 
D)  $7 n + 29$ 
E)  $7 n - 6$

Question 3

Write the first five terms of the sequence $a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }$ . Assume that n begins with 1.

Accepted Answer

A)  $a _ { 1 } = - \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = - \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = - \frac { 1 } { 26 }$ 
B)  $a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }$ 
C)  $a _ { 1 } = - 1 , a _ { 2 } = \frac { 1 } { 4 } , a _ { 3 } = - \frac { 1 } { 9 } , a _ { 4 } = \frac { 1 } { 16 } , a _ { 5 } = - \frac { 1 } { 25 }$ 
D)  $a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = - \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = - \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }$ 
E)  $a _ { 1 } = 1 , a _ { 2 } = - \frac { 1 } { 4 } , a _ { 3 } = \frac { 1 } { 9 } , a _ { 4 } = - \frac { 1 } { 16 } , a _ { 5 } = \frac { 1 } { 25 }$ 
A)  $a _ { 1 } = - \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = - \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = - \frac { 1 } { 26 }$ 
B)  $a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }$ 
C)  $a _ { 1 } = - 1 , a _ { 2 } = \frac { 1 } { 4 } , a _ { 3 } = - \frac { 1 } { 9 } , a _ { 4 } = \frac { 1 } { 16 } , a _ { 5 } = - \frac { 1 } { 25 }$ 
D)  $a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = - \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = - \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }$ 
E)  $a _ { 1 } = 1 , a _ { 2 } = - \frac { 1 } { 4 } , a _ { 3 } = \frac { 1 } { 9 } , a _ { 4 } = - \frac { 1 } { 16 } , a _ { 5 } = \frac { 1 } { 25 }$

Question 4

Write an expression for the n th term of the sequence $4 , \frac { 4 } { 2 } , \frac { 4 } { 6 } , \frac { 4 } { 24 } , \frac { 4 } { 120 } , \ldots$ Assume that n begins with 1.

Accepted Answer

A)  $a _ { n } = 4 + \frac { 1 } { n ! }$ 
B)  $a _ { n } = \frac { 4 } { ( n + 1 ) }$ 
C)  $a _ { n } = \frac { 4 } { n ( n + 1 ) }$ 
D)  $a _ { n } = \frac { 4 } { n ! }$ 
E)  $a _ { n } = 4 + \frac { 1 } { ( n + 1 ) ! }$ 
A)  $a _ { n } = 4 + \frac { 1 } { n ! }$ 
B)  $a _ { n } = \frac { 4 } { ( n + 1 ) }$ 
C)  $a _ { n } = \frac { 4 } { n ( n + 1 ) }$ 
D)  $a _ { n } = \frac { 4 } { n ! }$ 
E)  $a _ { n } = 4 + \frac { 1 } { ( n + 1 ) ! }$

Question 5

Determine whether the sequence is arithmetic. If so, find the common difference. $\frac { 1 } { 5 } , \frac { 3 } { 5 } , \frac { 9 } { 5 } , \frac { 27 } { 5 } , \frac { 81 } { 5 } , \ldots$

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 9 } { 5 }$ 
C)  2
5 
D)  $\frac { 81 } { 5 }$ 
E) The sequence is not arithmetic. 
A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 9 } { 5 }$ 
C)  2
5 
D)  $\frac { 81 } { 5 }$ 
E) The sequence is not arithmetic.

Question 6

Find the coefficient of the term $x ^ { 6 } y ^ { 8 }$ in the expansion of the binomial $( x - y ) ^ { 14 }$ .

Accepted Answer

A)  $3,003$ 
B)  $2,997$ 
C)  $- 2,979$ 
D)  $- 2,985$ 
E)  $- 2,973$ 
A)  $3,003$ 
B)  $2,997$ 
C)  $- 2,979$ 
D)  $- 2,985$ 
E)  $- 2,973$

Question 7

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $4,-10,25,-\frac{125}{2}, \ldots$

Accepted Answer

A)  $a_{n}=2\left(-\frac{5}{2}\right)^{n-1}$ 
B)  $a_{n}=2\left(-\frac{5}{2}\right)^{n-2}$ 
C)  $a_{n}=4\left(-\frac{5}{2}\right)^{n-1}$ 
D)  $a_{n}=-2\left(-\frac{5}{2}\right)^{n}$ 
E)  $a_{n}=-4\left(-\frac{5}{2}\right)^{n}$ 
A)  $a_{n}=2\left(-\frac{5}{2}\right)^{n-1}$ 
B)  $a_{n}=2\left(-\frac{5}{2}\right)^{n-2}$ 
C)  $a_{n}=4\left(-\frac{5}{2}\right)^{n-1}$ 
D)  $a_{n}=-2\left(-\frac{5}{2}\right)^{n}$ 
E)  $a_{n}=-4\left(-\frac{5}{2}\right)^{n}$

Question 8

Find the common difference of the arithmetic sequence $\frac { 17 } { 8 } , \frac { 7 } { 4 } , \frac { 11 } { 8 } , 1 , \frac { 5 } { 8 } , \ldots$

Accepted Answer

A)  $\frac { 11 } { 4 }$ 
B)  $- \frac { 3 } { 8 }$ 
C)  $- \frac { 3 } { 4 }$ 
D)  $- \frac { 7 } { 4 }$ 
E)  $\frac { 11 } { 8 }$ 
A)  $\frac { 11 } { 4 }$ 
B)  $- \frac { 3 } { 8 }$ 
C)  $- \frac { 3 } { 4 }$ 
D)  $- \frac { 7 } { 4 }$ 
E)  $\frac { 11 } { 8 }$

Question 9

Find the partial sum of $\sum _ { k = 1 } ^ { 5 } \frac { n } { 10 }$ .

Accepted Answer

A)  -13.75 
B)  0.25 
C)  2.5 
D)  1.5 
E)  3 
A)  -13.75 
B)  0.25 
C)  2.5 
D)  1.5 
E)  3

Question 10

Find the sum. $\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}$

Accepted Answer

A)  $\frac{8}{11}$ 
B)  $\frac{3}{14}$ 
C)  $\frac{5}{8}$ 
D)  $\frac{8}{5}$ 
E)  $\frac{3}{5}$ 
A)  $\frac{8}{11}$ 
B)  $\frac{3}{14}$ 
C)  $\frac{5}{8}$ 
D)  $\frac{8}{5}$ 
E)  $\frac{3}{5}$

Question 11

Write an expression for the n th term of the sequence $3,8,13,18,23 , \ldots$ Assume that n begins with 1.

Accepted Answer

A)  $a _ { n } = 3 + 5 n$ 
B)  $a _ { n } = 3 + 6 n$ 
C)  $a _ { n } = 3 + 6 ( n + 1 )$ 
D)  $a _ { n } = 3 + 5 ( n - 1 )$ 
E)  $a _ { n } = 3 + 5 ( n + 1 )$ 
A)  $a _ { n } = 3 + 5 n$ 
B)  $a _ { n } = 3 + 6 n$ 
C)  $a _ { n } = 3 + 6 ( n + 1 )$ 
D)  $a _ { n } = 3 + 5 ( n - 1 )$ 
E)  $a _ { n } = 3 + 5 ( n + 1 )$

Question 12

Find the common ratio of the geometric sequence. $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16},...$

Accepted Answer

A)  $-\frac{1}{8}$ 
B)  $\frac{1}{4}$ 
C)  $\frac{1}{2}$ 
D)  $-\frac{1}{2}$ 
E)  $-\frac{1}{4}$ 
A)  $-\frac{1}{8}$ 
B)  $\frac{1}{4}$ 
C)  $\frac{1}{2}$ 
D)  $-\frac{1}{2}$ 
E)  $-\frac{1}{4}$

Question 13

In your new job as an accountant you are told that your starting salary will be $\$ 36,000$ with an increase of $\$ 2500$ at the end of each of the first $4$ years. How much will you be paid through the end of your first 5 years of employment with the company?

Accepted Answer

A) $ $211,250$ 
B) $ $164,000$ 
C) $ $159,000$ 
D) $ $205,000$ 
E) $ $198,750$ 
A) $ $211,250$ 
B) $ $164,000$ 
C) $ $159,000$ 
D) $ $205,000$ 
E) $ $198,750$

Question 14

Write the first five terms of the sequence $a _ { n } = - 4 - \frac { 1 } { 3 ^ { n } }$ . Assume that n begins with 1.

Accepted Answer

A)  $a _ { 1 } = - \frac { 11 } { 3 } , a _ { 2 } = - \frac { 35 } { 9 } , a _ { 3 } = - \frac { 107 } { 27 } , a _ { 4 } = - \frac { 323 } { 81 } , a _ { 5 } = - \frac { 971 } { 243 }$ 
B)  $a _ { 1 } = - \frac { 13 } { 3 } , a _ { 2 } = - \frac { 37 } { 9 } , a _ { 3 } = - \frac { 109 } { 27 } , a _ { 4 } = - \frac { 325 } { 81 } , a _ { 5 } = - \frac { 973 } { 243 }$ 
C)  $a _ { 1 } = \frac { 11 } { 3 } , a _ { 2 } = \frac { 35 } { 9 } , a _ { 3 } = \frac { 107 } { 27 } , a _ { 4 } = \frac { 323 } { 81 } , a _ { 5 } = \frac { 971 } { 243 }$ 
D)  $a _ { 1 } = - 3 , a _ { 2 } = \frac { 11 } { 3 } , a _ { 3 } = \frac { 35 } { 9 } , a _ { 4 } = \frac { 107 } { 27 } , a _ { 5 } = \frac { 323 } { 81 }$ 
E)  $a _ { 1 } = - 5 , a _ { 2 } = - \frac { 13 } { 3 } , a _ { 3 } = - \frac { 37 } { 9 } , a _ { 4 } = - \frac { 109 } { 27 } , a _ { 5 } = - \frac { 325 } { 81 }$ 
A)  $a _ { 1 } = - \frac { 11 } { 3 } , a _ { 2 } = - \frac { 35 } { 9 } , a _ { 3 } = - \frac { 107 } { 27 } , a _ { 4 } = - \frac { 323 } { 81 } , a _ { 5 } = - \frac { 971 } { 243 }$ 
B)  $a _ { 1 } = - \frac { 13 } { 3 } , a _ { 2 } = - \frac { 37 } { 9 } , a _ { 3 } = - \frac { 109 } { 27 } , a _ { 4 } = - \frac { 325 } { 81 } , a _ { 5 } = - \frac { 973 } { 243 }$ 
C)  $a _ { 1 } = \frac { 11 } { 3 } , a _ { 2 } = \frac { 35 } { 9 } , a _ { 3 } = \frac { 107 } { 27 } , a _ { 4 } = \frac { 323 } { 81 } , a _ { 5 } = \frac { 971 } { 243 }$ 
D)  $a _ { 1 } = - 3 , a _ { 2 } = \frac { 11 } { 3 } , a _ { 3 } = \frac { 35 } { 9 } , a _ { 4 } = \frac { 107 } { 27 } , a _ { 5 } = \frac { 323 } { 81 }$ 
E)  $a _ { 1 } = - 5 , a _ { 2 } = - \frac { 13 } { 3 } , a _ { 3 } = - \frac { 37 } { 9 } , a _ { 4 } = - \frac { 109 } { 27 } , a _ { 5 } = - \frac { 325 } { 81 }$

Question 15

Determine whether the sequence is geometric. If so, find the common ratio. $1024,256,64,16, \ldots$

Accepted Answer

A) -4 
B) 4 
C)  $-\frac{1}{4}$ 
D)  $\frac{1}{4}$ 
E) not geometric 
A) -4 
B) 4 
C)  $-\frac{1}{4}$ 
D)  $\frac{1}{4}$ 
E) not geometric

Question 16

Find the partial sum. $\sum_{i-1}^{8} 3\left(-\frac{1}{4}\right)^{i-1}$

Accepted Answer

A)  $\frac{9}{16,384}$ 
B)  $\frac{291}{16,384}$ 
C)  $\frac{39,321}{16,384}$ 
D)  $\frac{3}{16,384}$ 
E)  $\frac{99}{16,384}$ 
A)  $\frac{9}{16,384}$ 
B)  $\frac{291}{16,384}$ 
C)  $\frac{39,321}{16,384}$ 
D)  $\frac{3}{16,384}$ 
E)  $\frac{99}{16,384}$

Question 17

Write the sum using sigma notation. Begin with $k = 1$ . $\frac { 1 } { 1 ^ { 3 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 3 ^ { 3 } } + \frac { 1 } { 4 ^ { 3 } } + \ldots + \frac { 1 } { 16 ^ { 3 } }$

Accepted Answer

A)  $\sum _ { k = 1 } ^ { 15 } \frac { 1 } { k ^ { 3 } }$ 
B)  $\sum _ { k = 1 } ^ { 15 } \frac { 1 } { ( k - 1 ) ^ { 3 } }$ 
C)  $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { ( k - 1 ) ^ { 3 } }$ 
D)  $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { ( k + 1 ) ^ { 3 } }$ 
E)  $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { k ^ { 3 } }$ 
A)  $\sum _ { k = 1 } ^ { 15 } \frac { 1 } { k ^ { 3 } }$ 
B)  $\sum _ { k = 1 } ^ { 15 } \frac { 1 } { ( k - 1 ) ^ { 3 } }$ 
C)  $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { ( k - 1 ) ^ { 3 } }$ 
D)  $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { ( k + 1 ) ^ { 3 } }$ 
E)  $\sum _ { k = 1 } ^ { 16 } \frac { 1 } { k ^ { 3 } }$

Question 18

Use Pascal s Triangle to expand the expression $( x + 2 ) ^ { 5 }$ .

Accepted Answer

A)  $x ^ { 5 } + 5 x ^ { 4 } + 10 x ^ { 3 } + 10 x ^ { 2 } + 5 x + 2$ 
B)  $x ^ { 5 } + 5 x ^ { 4 } + 10 x ^ { 3 } + 10 x ^ { 2 } + 5 x + 32$ 
C)  $x ^ { 5 } + 32$ 
D)  $x ^ { 5 } + 2 x ^ { 4 } + 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x + 2$ 
E)  $x ^ { 5 } + 10 x ^ { 4 } + 40 x ^ { 3 } + 80 x ^ { 2 } + 80 x + 32$ 
A)  $x ^ { 5 } + 5 x ^ { 4 } + 10 x ^ { 3 } + 10 x ^ { 2 } + 5 x + 2$ 
B)  $x ^ { 5 } + 5 x ^ { 4 } + 10 x ^ { 3 } + 10 x ^ { 2 } + 5 x + 32$ 
C)  $x ^ { 5 } + 32$ 
D)  $x ^ { 5 } + 2 x ^ { 4 } + 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x + 2$ 
E)  $x ^ { 5 } + 10 x ^ { 4 } + 40 x ^ { 3 } + 80 x ^ { 2 } + 80 x + 32$

Question 19

Find a formula for the n th term of the arithmetic sequence. $a _ { 1 } = 75 , d = - 8$

Accepted Answer

A)  $a _ { n } = - 8 n - 83$ 
B)  $a _ { n } = - 8 n + 83$ 
C)  $a _ { n } = 8 n + 75$ 
D)  $a _ { n } = - 8 n + 67$ 
E)  $a _ { n } = - 8 n + 75$ 
A)  $a _ { n } = - 8 n - 83$ 
B)  $a _ { n } = - 8 n + 83$ 
C)  $a _ { n } = 8 n + 75$ 
D)  $a _ { n } = - 8 n + 67$ 
E)  $a _ { n } = - 8 n + 75$

Question 20

Find $a_{5}$ of the geometric sequence, given $a_{1}=9$ and $a_{2}=8$

Accepted Answer

A)  $\frac{6561}{4096}$ 
B)  $\frac{4096}{6561}$ 
C)  $\frac{729}{512}$ 
D)  $\frac { 4096 } { 729 }$ 
E)  $\frac { 6561 } { 512 }$ 
A)  $\frac{6561}{4096}$ 
B)  $\frac{4096}{6561}$ 
C)  $\frac{729}{512}$ 
D)  $\frac { 4096 } { 729 }$ 
E)  $\frac { 6561 } { 512 }$

Use the Binomial Theorem to expand the expression $( u - 2 v ) ^ { 3 }$ .

Find a formula for the n th term of the arithmetic sequence. $a _ { 5 } = 22 , a _ { 6 } = 29$

Write the first five terms of the sequence $a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }$ . Assume that n begins with 1.

Write an expression for the n th term of the sequence $4 , \frac { 4 } { 2 } , \frac { 4 } { 6 } , \frac { 4 } { 24 } , \frac { 4 } { 120 } , \ldots$ Assume that n begins with 1.

Determine whether the sequence is arithmetic. If so, find the common difference. $\frac { 1 } { 5 } , \frac { 3 } { 5 } , \frac { 9 } { 5 } , \frac { 27 } { 5 } , \frac { 81 } { 5 } , \ldots$

Find the coefficient of the term $x ^ { 6 } y ^ { 8 }$ in the expansion of the binomial $( x - y ) ^ { 14 }$ .

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $4,-10,25,-\frac{125}{2}, \ldots$

Find the common difference of the arithmetic sequence $\frac { 17 } { 8 } , \frac { 7 } { 4 } , \frac { 11 } { 8 } , 1 , \frac { 5 } { 8 } , \ldots$

Find the partial sum of $\sum _ { k = 1 } ^ { 5 } \frac { n } { 10 }$ .

Find the sum. $\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}$

Write an expression for the n th term of the sequence $3,8,13,18,23 , \ldots$ Assume that n begins with 1.

Find the common ratio of the geometric sequence. $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16},...$

In your new job as an accountant you are told that your starting salary will be $\$ 36,000$ with an increase of $\$ 2500$ at the end of each of the first $4$ years. How much will you be paid through the end of your first 5 years of employment with the company?

Write the first five terms of the sequence $a _ { n } = - 4 - \frac { 1 } { 3 ^ { n } }$ . Assume that n begins with 1.

Determine whether the sequence is geometric. If so, find the common ratio. $1024,256,64,16, \ldots$

Find the partial sum. $\sum_{i-1}^{8} 3\left(-\frac{1}{4}\right)^{i-1}$

Write the sum using sigma notation. Begin with $k = 1$ . $\frac { 1 } { 1 ^ { 3 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 3 ^ { 3 } } + \frac { 1 } { 4 ^ { 3 } } + \ldots + \frac { 1 } { 16 ^ { 3 } }$

Use Pascal s Triangle to expand the expression $( x + 2 ) ^ { 5 }$ .

Find a formula for the n th term of the arithmetic sequence. $a _ { 1 } = 75 , d = - 8$

Find $a_{5}$ of the geometric sequence, given $a_{1}=9$ and $a_{2}=8$

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Exam 11: Sequences, Series, and the Binomial Theorem

Use the Binomial Theorem to expand the expression (u−2v)3( u - 2 v ) ^ { 3 }(u−2v)3 .

Find a formula for the n th term of the arithmetic sequence. a5=22,a6=29a _ { 5 } = 22 , a _ { 6 } = 29a5​=22,a6​=29

Write the first five terms of the sequence an=(−1)n+4n2+1a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }an​=n2+1(−1)n+4​ . Assume that n begins with 1.

Write an expression for the n th term of the sequence 4,42,46,424,4120,…4 , \frac { 4 } { 2 } , \frac { 4 } { 6 } , \frac { 4 } { 24 } , \frac { 4 } { 120 } , \ldots4,24​,64​,244​,1204​,… Assume that n begins with 1.

Determine whether the sequence is arithmetic. If so, find the common difference. 15,35,95,275,815,…\frac { 1 } { 5 } , \frac { 3 } { 5 } , \frac { 9 } { 5 } , \frac { 27 } { 5 } , \frac { 81 } { 5 } , \ldots51​,53​,59​,527​,581​,…

Find the coefficient of the term x6y8x ^ { 6 } y ^ { 8 }x6y8 in the expansion of the binomial (x−y)14( x - y ) ^ { 14 }(x−y)14 .

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. 4,−10,25,−1252,…4,-10,25,-\frac{125}{2}, \ldots4,−10,25,−2125​,…

Find the common difference of the arithmetic sequence 178,74,118,1,58,…\frac { 17 } { 8 } , \frac { 7 } { 4 } , \frac { 11 } { 8 } , 1 , \frac { 5 } { 8 } , \ldots817​,47​,811​,1,85​,…

Find the partial sum of ∑k=15n10\sum _ { k = 1 } ^ { 5 } \frac { n } { 10 }∑k=15​10n​ .

Find the sum. ∑n=0∞(−38)n\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}∑n=0∞​(−83​)n

Write an expression for the n th term of the sequence 3,8,13,18,23,…3,8,13,18,23 , \ldots3,8,13,18,23,… Assume that n begins with 1.

Find the common ratio of the geometric sequence. 12,14,18,116,...\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16},...21​,41​,81​,161​,...

In your new job as an accountant you are told that your starting salary will be $36,000\$ 36,000$36,000 with an increase of $2500\$ 2500$2500 at the end of each of the first 444 years. How much will you be paid through the end of your first 5 years of employment with the company?

Write the first five terms of the sequence an=−4−13na _ { n } = - 4 - \frac { 1 } { 3 ^ { n } }an​=−4−3n1​ . Assume that n begins with 1.

Determine whether the sequence is geometric. If so, find the common ratio. 1024,256,64,16,…1024,256,64,16, \ldots1024,256,64,16,…

Find the partial sum. ∑i−183(−14)i−1\sum_{i-1}^{8} 3\left(-\frac{1}{4}\right)^{i-1}∑i−18​3(−41​)i−1

Write the sum using sigma notation. Begin with k=1k = 1k=1 . 113+123+133+143+…+1163\frac { 1 } { 1 ^ { 3 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 3 ^ { 3 } } + \frac { 1 } { 4 ^ { 3 } } + \ldots + \frac { 1 } { 16 ^ { 3 } }131​+231​+331​+431​+…+1631​

Use Pascal s Triangle to expand the expression (x+2)5( x + 2 ) ^ { 5 }(x+2)5 .

Find a formula for the n th term of the arithmetic sequence. a1=75,d=−8a _ { 1 } = 75 , d = - 8a1​=75,d=−8

Find a5a_{5}a5​ of the geometric sequence, given a1=9a_{1}=9a1​=9 and a2=8a_{2}=8a2​=8

Fundamentals of Algebra

Linear Equations and Inequalities

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Use the Binomial Theorem to expand the expression $( u - 2 v ) ^ { 3 }$ .

Find a formula for the n th term of the arithmetic sequence. $a _ { 5 } = 22 , a _ { 6 } = 29$

Write the first five terms of the sequence $a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }$ . Assume that n begins with 1.

Write an expression for the n th term of the sequence $4 , \frac { 4 } { 2 } , \frac { 4 } { 6 } , \frac { 4 } { 24 } , \frac { 4 } { 120 } , \ldots$ Assume that n begins with 1.

Determine whether the sequence is arithmetic. If so, find the common difference. $\frac { 1 } { 5 } , \frac { 3 } { 5 } , \frac { 9 } { 5 } , \frac { 27 } { 5 } , \frac { 81 } { 5 } , \ldots$

Find the coefficient of the term $x ^ { 6 } y ^ { 8 }$ in the expansion of the binomial $( x - y ) ^ { 14 }$ .

Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. $4,-10,25,-\frac{125}{2}, \ldots$

Find the common difference of the arithmetic sequence $\frac { 17 } { 8 } , \frac { 7 } { 4 } , \frac { 11 } { 8 } , 1 , \frac { 5 } { 8 } , \ldots$

Find the partial sum of $\sum _ { k = 1 } ^ { 5 } \frac { n } { 10 }$ .

Find the sum. $\sum_{n=0}^{\infty}\left(-\frac{3}{8}\right)^{n}$

Write an expression for the n th term of the sequence $3,8,13,18,23 , \ldots$ Assume that n begins with 1.

Find the common ratio of the geometric sequence. $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16},...$

In your new job as an accountant you are told that your starting salary will be $\$ 36,000$ with an increase of $\$ 2500$ at the end of each of the first $4$ years. How much will you be paid through the end of your first 5 years of employment with the company?

Write the first five terms of the sequence $a _ { n } = - 4 - \frac { 1 } { 3 ^ { n } }$ . Assume that n begins with 1.

Determine whether the sequence is geometric. If so, find the common ratio. $1024,256,64,16, \ldots$

Find the partial sum. $\sum_{i-1}^{8} 3\left(-\frac{1}{4}\right)^{i-1}$

Write the sum using sigma notation. Begin with $k = 1$ . $\frac { 1 } { 1 ^ { 3 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 3 ^ { 3 } } + \frac { 1 } { 4 ^ { 3 } } + \ldots + \frac { 1 } { 16 ^ { 3 } }$

Use Pascal s Triangle to expand the expression $( x + 2 ) ^ { 5 }$ .

Find a formula for the n th term of the arithmetic sequence. $a _ { 1 } = 75 , d = - 8$

Find $a_{5}$ of the geometric sequence, given $a_{1}=9$ and $a_{2}=8$