Question 1

Find the sum. $$\sum _ { j = 1 } ^ { 6 } \frac { j + 3 } { j }$$

Accepted Answer

A)  $\frac { 267 } { 20 }$ 
B)  39 
C)  $\frac { 13 } { 2 }$ 
D)  $\frac { 167 } { 20 }$ 
A)  $\frac { 267 } { 20 }$ 
B)  39 
C)  $\frac { 13 } { 2 }$ 
D)  $\frac { 167 } { 20 }$

Question 2

List the terms of the sequence. $$a _ { n } = n \left( n ^ { 3 } + 9 \right) , 1 \leq n \leq 4$$

Accepted Answer

A)  $11,17,21,25$ 
B)  $10,30,54,84$ 
C)  $10,34,108,292$ 
D)  $11,19,39,77$ 
A)  $11,17,21,25$ 
B)  $10,30,54,84$ 
C)  $10,34,108,292$ 
D)  $11,19,39,77$

Question 3

A home purchased for $105,000 increases by 3% of its value each year. The value of the home after n years is given by $a _ { n } = 105,000 ( 1.03 ) ^ { n } \text { for } n \geq 1$ Find the value of the home after 5 years by computing $a _ { 5 }$ . Round to the nearest dollar.

Accepted Answer

A)  $a _ { 5 } = \$ 121,724$ 
B)  $a _ { 5 } = \$ 3,898,580$ 
C)  $a _ { 5 } = \$ 389,858$ 
D)  $a _ { 5 } = \$ 1,217,238$ 
A)  $a _ { 5 } = \$ 121,724$ 
B)  $a _ { 5 } = \$ 3,898,580$ 
C)  $a _ { 5 } = \$ 389,858$ 
D)  $a _ { 5 } = \$ 1,217,238$

Question 4

Determine the sum of the infinite series, if it exists. $$- 28 + 7 + \left( - \frac { 7 } { 4 } \right) + \frac { 7 } { 16 } + \ldots$$

Accepted Answer

A)  $- \frac { 112 } { 3 }$ 
B)  $- \frac { 112 } { 11 }$ 
C)  Sum does not exist 
D)  $- \frac { 112 } { 5 }$ 
A)  $- \frac { 112 } { 3 }$ 
B)  $- \frac { 112 } { 11 }$ 
C)  Sum does not exist 
D)  $- \frac { 112 } { 5 }$

Question 5

Use the binomial theorem to expand the binomial. $$( 4 x - y ) ^ { 4 }$$

Accepted Answer

A)  $256 x ^ { 4 } - 256 x ^ { 3 } y - 16 x y ^ { 3 } + y ^ { 4 }$ 
B)  $4 x ^ { 4 } - 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } - 4 x y ^ { 3 } + y ^ { 4 }$ 
C)  $256 x ^ { 4 } - 256 x ^ { 3 } y + 96 x ^ { 2 } y ^ { 2 } - 16 x y ^ { 3 } + y ^ { 4 }$ 
D)  $4 x ^ { 4 } - 4 x ^ { 3 } y - 4 x y ^ { 3 } + y ^ { 4 }$ 
A)  $256 x ^ { 4 } - 256 x ^ { 3 } y - 16 x y ^ { 3 } + y ^ { 4 }$ 
B)  $4 x ^ { 4 } - 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } - 4 x y ^ { 3 } + y ^ { 4 }$ 
C)  $256 x ^ { 4 } - 256 x ^ { 3 } y + 96 x ^ { 2 } y ^ { 2 } - 16 x y ^ { 3 } + y ^ { 4 }$ 
D)  $4 x ^ { 4 } - 4 x ^ { 3 } y - 4 x y ^ { 3 } + y ^ { 4 }$

Question 6

Find the nth term of the geometric sequence. -8, 16, -32, 64, ...

Accepted Answer

A)  $- 8 ( - 2 ) ^ { n - 1 }$ 
B)  $- 2 ( - 8 ) ^ { n }$ 
C)  $- 2 ( - 8 ) ^ { n - 1 }$ 
D)  $- 8 ( - 2 ) ^ { n }$ 
A)  $- 8 ( - 2 ) ^ { n - 1 }$ 
B)  $- 2 ( - 8 ) ^ { n }$ 
C)  $- 2 ( - 8 ) ^ { n - 1 }$ 
D)  $- 8 ( - 2 ) ^ { n }$

Question 7

Find a formula for the nth term of the sequence. $8,16,24,32 , \ldots$

Accepted Answer

A)  $a ^ { n } = 8 ( n - 1 )$ 
B)  $a ^ { n } = 8 n$ 
C)  $a ^ { n } = a ^ { n } = 8 ( n + 1 )$ 
D)  $a ^ { n } = 8 ^ { n }$ 
A)  $a ^ { n } = 8 ( n - 1 )$ 
B)  $a ^ { n } = 8 n$ 
C)  $a ^ { n } = a ^ { n } = 8 ( n + 1 )$ 
D)  $a ^ { n } = 8 ^ { n }$

Question 8

Find the indicated term of the geometric sequence. Given $a _ { 8 } = - 768$ and $r = 2$, find $a _ { 1 }$.

Accepted Answer

A)  12 
B)  $- 6$ 
C)  $- 12$ 
D)  6 
A)  12 
B)  $- 6$ 
C)  $- 12$ 
D)  6

Question 9

Write the first five terms of the arithmetic sequence. $$a _ { 1 } = 2 , d = \frac { 2 } { 3 }$$

Accepted Answer

A)  $\frac { 8 } { 3 } , \frac { 10 } { 3 } , 4 , \frac { 14 } { 3 } , \frac { 16 } { 3 }$ 
B)  $\frac { 4 } { 3 } , \frac { 8 } { 9 } , \frac { 16 } { 27 } , \frac { 32 } { 81 } , \frac { 64 } { 243 }$ 
C)  $2 , \frac { 4 } { 3 } , \frac { 8 } { 9 } , \frac { 16 } { 27 } , \frac { 32 } { 81 }$ 
D)  $2 , \frac { 8 } { 3 } , \frac { 10 } { 3 } , 4 , \frac { 14 } { 3 }$ 
A)  $\frac { 8 } { 3 } , \frac { 10 } { 3 } , 4 , \frac { 14 } { 3 } , \frac { 16 } { 3 }$ 
B)  $\frac { 4 } { 3 } , \frac { 8 } { 9 } , \frac { 16 } { 27 } , \frac { 32 } { 81 } , \frac { 64 } { 243 }$ 
C)  $2 , \frac { 4 } { 3 } , \frac { 8 } { 9 } , \frac { 16 } { 27 } , \frac { 32 } { 81 }$ 
D)  $2 , \frac { 8 } { 3 } , \frac { 10 } { 3 } , 4 , \frac { 14 } { 3 }$

Question 10

List the terms of the sequence. $$a _ { n } = ( - 1 ) ^ { n } \frac { n + 1 } { n - 6 } , 1 \leq n \leq 4$$

Accepted Answer

A)  $\frac { 5 } { 6 } , - \frac { 11 } { 6 } , \frac { 17 } { 6 } , - \frac { 23 } { 6 }$ 
B)  $\frac { 2 } { 5 } , - \frac { 3 } { 4 } , \frac { 4 } { 3 } , - \frac { 5 } { 2 }$ 
C)  $- \frac { 5 } { 6 } , \frac { 11 } { 6 } , - \frac { 17 } { 6 } , \frac { 23 } { 6 }$ 
D)  $- \frac { 2 } { 5 } , \frac { 3 } { 4 } , - \frac { 4 } { 3 } , \frac { 5 } { 2 }$ 
A)  $\frac { 5 } { 6 } , - \frac { 11 } { 6 } , \frac { 17 } { 6 } , - \frac { 23 } { 6 }$ 
B)  $\frac { 2 } { 5 } , - \frac { 3 } { 4 } , \frac { 4 } { 3 } , - \frac { 5 } { 2 }$ 
C)  $- \frac { 5 } { 6 } , \frac { 11 } { 6 } , - \frac { 17 } { 6 } , \frac { 23 } { 6 }$ 
D)  $- \frac { 2 } { 5 } , \frac { 3 } { 4 } , - \frac { 4 } { 3 } , \frac { 5 } { 2 }$

Question 11

Expand the binomial. Use Pascal's triangle to find the coefficients. $$\left( x ^ { 5 } + y \right) ^ { 6 }$$

Accepted Answer

A)  $x ^ { 11 } + 6 x ^ { 10 } y + 15 x ^ { 9 } y ^ { 2 } + 20 x ^ { 8 } y ^ { 3 } + 15 x ^ { 7 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
B)  $x ^ { 30 } + y ^ { 6 }$ 
C)  $x ^ { 30 } + 6 x ^ { 25 } y + 15 x ^ { 20 } y ^ { 2 } + 20 x ^ { 15 } y ^ { 3 } + 15 x ^ { 10 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
D)  $x ^ { 6 } + 6 x ^ { 5 } y + 15 x ^ { 4 } y ^ { 2 } + 20 x ^ { 3 } y ^ { 3 } + 15 x ^ { 2 } y ^ { 4 } + 6 x y ^ { 5 } + y ^ { 6 }$ 
A)  $x ^ { 11 } + 6 x ^ { 10 } y + 15 x ^ { 9 } y ^ { 2 } + 20 x ^ { 8 } y ^ { 3 } + 15 x ^ { 7 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
B)  $x ^ { 30 } + y ^ { 6 }$ 
C)  $x ^ { 30 } + 6 x ^ { 25 } y + 15 x ^ { 20 } y ^ { 2 } + 20 x ^ { 15 } y ^ { 3 } + 15 x ^ { 10 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 5 } + y ^ { 6 }$ 
D)  $x ^ { 6 } + 6 x ^ { 5 } y + 15 x ^ { 4 } y ^ { 2 } + 20 x ^ { 3 } y ^ { 3 } + 15 x ^ { 2 } y ^ { 4 } + 6 x y ^ { 5 } + y ^ { 6 }$

Question 12

Find the sum. $$\sum _ { j = 1 } ^ { 5 } j ( j + 8 )$$

Accepted Answer

A)  65 
B)  175 
C)  195 
D)  45 
A)  65 
B)  175 
C)  195 
D)  45

Question 13

Find the common difference d for the arithmetic sequence. 4, -5, -14, -23, -32, ...

Accepted Answer

A)  -4 
B)  4 
C)  9 
D)  -9 
A)  -4 
B)  4 
C)  9 
D)  -9

Question 14

Find the common difference d for the arithmetic sequence. -4, 4, 12, 20, 28, ...

Accepted Answer

A)  8 
B)  4 
C)  -8 
D)  -4 
A)  8 
B)  4 
C)  -8 
D)  -4

Question 15

Find the indicated term of the geometric sequence. Given $a _ { n } = 8 ( - 2 ) ^ { n - 1 }$, find $a _ { 5 }$.

Accepted Answer

A)  $- 2$ 
B)  128 
C)  $- 256$ 
D)  0 
A)  $- 2$ 
B)  128 
C)  $- 256$ 
D)  0

Question 16

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.
$\left( 4 - y ^ { 4 } \right) ^ { 5 }$

Accepted Answer

A)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 5 y ^ { 4 } + 10 y ^ { 8 } - 10 y ^ { 12 } + 5 y ^ { 16 } - y ^ { 20 }$ 
B)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 1280 y + 640 y ^ { 2 } - 160 y ^ { 3 } + 20 y ^ { 5 } - y ^ { 6 }$ 
C)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 1280 y ^ { 4 } + 640 y ^ { 8 } - 160 y ^ { 12 } + 20 y ^ { 16 } - y ^ { 20 }$ 
D)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 5 y + 10 y ^ { 2 } - 10 y ^ { 3 } + 5 y ^ { 4 } - y ^ { 6 }$ 
A)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 5 y ^ { 4 } + 10 y ^ { 8 } - 10 y ^ { 12 } + 5 y ^ { 16 } - y ^ { 20 }$ 
B)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 1280 y + 640 y ^ { 2 } - 160 y ^ { 3 } + 20 y ^ { 5 } - y ^ { 6 }$ 
C)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 1280 y ^ { 4 } + 640 y ^ { 8 } - 160 y ^ { 12 } + 20 y ^ { 16 } - y ^ { 20 }$ 
D)  $\left[ 4 + \left( - y ^ { 4 } \right) \right] ^ { 5 } ; 1024 - 5 y + 10 y ^ { 2 } - 10 y ^ { 3 } + 5 y ^ { 4 } - y ^ { 6 }$

Question 17

Write the series in summation notation. $$8 + 16 + 24 + 32 + 40$$

Accepted Answer

A)  $\sum _ { j = 1 } ^ { 5 } 8 j$ 
B)  $\sum _ { j = 1 } ^ { 5 } 8 ^ { j }$ 
C)  $\sum _ { j = 1 } ^ { 5 } 8 + j$ 
D)  $\sum _ { j = 1 } ^ { 5 } j ^ { 8 }$ 
A)  $\sum _ { j = 1 } ^ { 5 } 8 j$ 
B)  $\sum _ { j = 1 } ^ { 5 } 8 ^ { j }$ 
C)  $\sum _ { j = 1 } ^ { 5 } 8 + j$ 
D)  $\sum _ { j = 1 } ^ { 5 } j ^ { 8 }$

Question 18

Use the binomial theorem to expand the binomial. $$\left( \frac { a } { 4 } - b \right) ^ { 5 }$$

Accepted Answer

A)  $\frac { 1 } { 1024 } a ^ { 5 } - \frac { 5 } { 256 } a ^ { 4 } b + \frac { 5 } { 32 } a ^ { 3 } b ^ { 2 } - \frac { 5 } { 16 } a ^ { 3 } b ^ { 3 } + \frac { 5 } { 8 } a ^ { 2 } b ^ { 3 } - \frac { 5 } { 4 } a b ^ { 4 } + b ^ { 5 }$ 
B)  $\frac { 1 } { 4 } a ^ { 5 } - \frac { 5 } { 4 } a ^ { 4 } b + \frac { 5 } { 2 } a ^ { 3 } b ^ { 2 } - \frac { 5 } { 2 } a ^ { 2 } b ^ { 3 } - \frac { 5 } { 4 } a b ^ { 4 } - b ^ { 5 }$ 
C)  $\frac { 1 } { 1024 } a ^ { 5 } - \frac { 5 } { 256 } a ^ { 4 } b + \frac { 5 } { 32 } a ^ { 3 } b ^ { 2 } - \frac { 5 } { 8 } a ^ { 2 } b ^ { 3 } + \frac { 5 } { 4 } a b ^ { 4 } - b ^ { 5 }$ 
D)  $\frac { 1 } { 4 } a ^ { 5 } - \frac { 5 } { 4 } a ^ { 4 } b + \frac { 5 } { 2 } a ^ { 3 } b ^ { 2 } - 5 a ^ { 3 } b ^ { 3 } + \frac { 5 } { 2 } a ^ { 2 } b ^ { 3 } - \frac { 5 } { 4 } a b ^ { 4 } + b ^ { 5 }$ 
A)  $\frac { 1 } { 1024 } a ^ { 5 } - \frac { 5 } { 256 } a ^ { 4 } b + \frac { 5 } { 32 } a ^ { 3 } b ^ { 2 } - \frac { 5 } { 16 } a ^ { 3 } b ^ { 3 } + \frac { 5 } { 8 } a ^ { 2 } b ^ { 3 } - \frac { 5 } { 4 } a b ^ { 4 } + b ^ { 5 }$ 
B)  $\frac { 1 } { 4 } a ^ { 5 } - \frac { 5 } { 4 } a ^ { 4 } b + \frac { 5 } { 2 } a ^ { 3 } b ^ { 2 } - \frac { 5 } { 2 } a ^ { 2 } b ^ { 3 } - \frac { 5 } { 4 } a b ^ { 4 } - b ^ { 5 }$ 
C)  $\frac { 1 } { 1024 } a ^ { 5 } - \frac { 5 } { 256 } a ^ { 4 } b + \frac { 5 } { 32 } a ^ { 3 } b ^ { 2 } - \frac { 5 } { 8 } a ^ { 2 } b ^ { 3 } + \frac { 5 } { 4 } a b ^ { 4 } - b ^ { 5 }$ 
D)  $\frac { 1 } { 4 } a ^ { 5 } - \frac { 5 } { 4 } a ^ { 4 } b + \frac { 5 } { 2 } a ^ { 3 } b ^ { 2 } - 5 a ^ { 3 } b ^ { 3 } + \frac { 5 } { 2 } a ^ { 2 } b ^ { 3 } - \frac { 5 } { 4 } a b ^ { 4 } + b ^ { 5 }$

Question 19

Find the sum of the geometric series. 7 + (-14) + 28 + (-56) + 112

Accepted Answer

A)  21 
B)  -147 
C)  -35 
D)  77 
A)  21 
B)  -147 
C)  -35 
D)  77

Question 20

Determine the common ratio, r, for the geometric sequence. -6, 24, -96, 384, ...

Accepted Answer

A)  -30 
B)  4 
C)  30 
D)  -4 
A)  -30 
B)  4 
C)  30 
D)  -4

Find the sum. $\sum _ { j = 1 } ^ { 6 } \frac { j + 3 } { j }$

List the terms of the sequence. $a _ { n } = n \left( n ^ { 3 } + 9 \right) , 1 \leq n \leq 4$

A home purchased for $105,000 increases by 3% of its value each year. The value of the home after n years is given by $a _ { n } = 105,000 ( 1.03 ) ^ { n } \text { for } n \geq 1$ Find the value of the home after 5 years by computing $a _ { 5 }$ . Round to the nearest dollar.

Determine the sum of the infinite series, if it exists. $- 28 + 7 + \left( - \frac { 7 } { 4 } \right) + \frac { 7 } { 16 } + \ldots$

Use the binomial theorem to expand the binomial. $( 4 x - y ) ^ { 4 }$

Find the nth term of the geometric sequence. -8, 16, -32, 64, ...

Find a formula for the nth term of the sequence. $8,16,24,32 , \ldots$

Find the indicated term of the geometric sequence. Given $a _ { 8 } = - 768$ and $r = 2$ , find $a _ { 1 }$ .

Write the first five terms of the arithmetic sequence. $a _ { 1 } = 2 , d = \frac { 2 } { 3 }$

List the terms of the sequence. $a _ { n } = ( - 1 ) ^ { n } \frac { n + 1 } { n - 6 } , 1 \leq n \leq 4$

Expand the binomial. Use Pascal's triangle to find the coefficients. $\left( x ^ { 5 } + y \right) ^ { 6 }$

Find the sum. $\sum _ { j = 1 } ^ { 5 } j ( j + 8 )$

Find the common difference d for the arithmetic sequence. 4, -5, -14, -23, -32, ...

Find the common difference d for the arithmetic sequence. -4, 4, 12, 20, 28, ...

Find the indicated term of the geometric sequence. Given $a _ { n } = 8 ( - 2 ) ^ { n - 1 }$ , find $a _ { 5 }$ .

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. $\left( 4 - y ^ { 4 } \right) ^ { 5 }$

Write the series in summation notation. $8 + 16 + 24 + 32 + 40$

Use the binomial theorem to expand the binomial. $\left( \frac { a } { 4 } - b \right) ^ { 5 }$

Find the sum of the geometric series. 7 + (-14) + 28 + (-56) + 112

Determine the common ratio, r, for the geometric sequence. -6, 24, -96, 384, ...

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

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Exam 10: Binomial Expansions, Sequences, and Series

Find the sum. ∑j=16j+3j\sum _ { j = 1 } ^ { 6 } \frac { j + 3 } { j }∑j=16​jj+3​

List the terms of the sequence. an=n(n3+9),1≤n≤4a _ { n } = n \left( n ^ { 3 } + 9 \right) , 1 \leq n \leq 4an​=n(n3+9),1≤n≤4

Determine the sum of the infinite series, if it exists. −28+7+(−74)+716+…- 28 + 7 + \left( - \frac { 7 } { 4 } \right) + \frac { 7 } { 16 } + \ldots−28+7+(−47​)+167​+…

Use the binomial theorem to expand the binomial. (4x−y)4( 4 x - y ) ^ { 4 }(4x−y)4

Find the nth term of the geometric sequence. -8, 16, -32, 64, ...

Find a formula for the nth term of the sequence. 8,16,24,32,…8,16,24,32 , \ldots8,16,24,32,…

Find the indicated term of the geometric sequence. Given a8=−768a _ { 8 } = - 768a8​=−768 and r=2r = 2r=2 , find a1a _ { 1 }a1​ .

Write the first five terms of the arithmetic sequence. a1=2,d=23a _ { 1 } = 2 , d = \frac { 2 } { 3 }a1​=2,d=32​

List the terms of the sequence. an=(−1)nn+1n−6,1≤n≤4a _ { n } = ( - 1 ) ^ { n } \frac { n + 1 } { n - 6 } , 1 \leq n \leq 4an​=(−1)nn−6n+1​,1≤n≤4

Expand the binomial. Use Pascal's triangle to find the coefficients. (x5+y)6\left( x ^ { 5 } + y \right) ^ { 6 }(x5+y)6

Find the sum. ∑j=15j(j+8)\sum _ { j = 1 } ^ { 5 } j ( j + 8 )∑j=15​j(j+8)

Find the common difference d for the arithmetic sequence. 4, -5, -14, -23, -32, ...

Find the common difference d for the arithmetic sequence. -4, 4, 12, 20, 28, ...

Find the indicated term of the geometric sequence. Given an=8(−2)n−1a _ { n } = 8 ( - 2 ) ^ { n - 1 }an​=8(−2)n−1 , find a5a _ { 5 }a5​ .

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. (4−y4)5\left( 4 - y ^ { 4 } \right) ^ { 5 }(4−y4)5

Write the series in summation notation. 8+16+24+32+408 + 16 + 24 + 32 + 408+16+24+32+40

Use the binomial theorem to expand the binomial. (a4−b)5\left( \frac { a } { 4 } - b \right) ^ { 5 }(4a​−b)5

Find the sum of the geometric series. 7 + (-14) + 28 + (-56) + 112

Determine the common ratio, r, for the geometric sequence. -6, 24, -96, 384, ...

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. $\sum _ { j = 1 } ^ { 6 } \frac { j + 3 } { j }$

List the terms of the sequence. $a _ { n } = n \left( n ^ { 3 } + 9 \right) , 1 \leq n \leq 4$

Determine the sum of the infinite series, if it exists. $- 28 + 7 + \left( - \frac { 7 } { 4 } \right) + \frac { 7 } { 16 } + \ldots$

Use the binomial theorem to expand the binomial. $( 4 x - y ) ^ { 4 }$

Find a formula for the nth term of the sequence. $8,16,24,32 , \ldots$

Find the indicated term of the geometric sequence. Given $a _ { 8 } = - 768$ and $r = 2$ , find $a _ { 1 }$ .

Write the first five terms of the arithmetic sequence. $a _ { 1 } = 2 , d = \frac { 2 } { 3 }$

List the terms of the sequence. $a _ { n } = ( - 1 ) ^ { n } \frac { n + 1 } { n - 6 } , 1 \leq n \leq 4$

Expand the binomial. Use Pascal's triangle to find the coefficients. $\left( x ^ { 5 } + y \right) ^ { 6 }$

Find the sum. $\sum _ { j = 1 } ^ { 5 } j ( j + 8 )$

Find the indicated term of the geometric sequence. Given $a _ { n } = 8 ( - 2 ) ^ { n - 1 }$ , find $a _ { 5 }$ .

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. $\left( 4 - y ^ { 4 } \right) ^ { 5 }$

Write the series in summation notation. $8 + 16 + 24 + 32 + 40$

Use the binomial theorem to expand the binomial. $\left( \frac { a } { 4 } - b \right) ^ { 5 }$