Question 1

Write the series in summation notation. $$- \frac { 1 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 27 } + \frac { 1 } { 81 }$$

Accepted Answer

A)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j + 1 } \frac { 1 } { 3 ^ { j } }$ 
B)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j } \frac { 1 } { 3 j }$ 
C)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j } \frac { 1 } { 3 ^ { j } }$ 
D)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j + 1 } \frac { 1 } { 3 j }$ 
A)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j + 1 } \frac { 1 } { 3 ^ { j } }$ 
B)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j } \frac { 1 } { 3 j }$ 
C)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j } \frac { 1 } { 3 ^ { j } }$ 
D)  $\sum _ { j = 1 } ^ { 4 } ( - 1 ) ^ { j + 1 } \frac { 1 } { 3 j }$ C

Question 2

Write the nth term of the arithmetic sequence. 3, -2, -7, -12, -17, ...

Accepted Answer

A)  $3 - 5 ^ { n }$ 
B)  $3 - 5 n$ 
C)  $8 - 5 n$ 
D)  $8 - 5 ^ { n }$ 
A)  $3 - 5 ^ { n }$ 
B)  $3 - 5 n$ 
C)  $8 - 5 n$ 
D)  $8 - 5 ^ { n }$ C

Question 3

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

Accepted Answer

A)  $- 1,2,5,8,11$ 
B)  $- 1,2,8,26,80$ 
C)  $3,2,1,0 , - 1$ 
D)  $3,2,4,2,4$ 
A)  $- 1,2,5,8,11$ 
B)  $- 1,2,8,26,80$ 
C)  $3,2,1,0 , - 1$ 
D)  $3,2,4,2,4$ A

Question 4

Find the sum. $$\sum _ { i = 1 } ^ { 5 } \left( 2 i ^ { 2 } \right)$$

Accepted Answer

A)  75 
B)  150 
C)  110 
D)  220 
A)  75 
B)  150 
C)  110 
D)  220

Question 5

Find the nth term of the geometric sequence. $$\frac { 1 } { 2 } , 2,8,32 , \ldots$$

Accepted Answer

A)  $\frac { 1 } { 4 } ( 2 ) ^ { n - 1 }$ 
B)  $\frac { 1 } { 2 } ( 4 ) ^ { n - 1 }$ 
C)  $\frac { 1 } { 4 } ( 2 ) ^ { n }$ 
D)  $\frac { 1 } { 2 } ( 4 ) ^ { n }$ 
A)  $\frac { 1 } { 4 } ( 2 ) ^ { n - 1 }$ 
B)  $\frac { 1 } { 2 } ( 4 ) ^ { n - 1 }$ 
C)  $\frac { 1 } { 4 } ( 2 ) ^ { n }$ 
D)  $\frac { 1 } { 2 } ( 4 ) ^ { n }$

Question 6

A ball drops from a height of 6 ft. With each bounce, the ball rebounds to $\frac { 2 } { 5 }$ of its height. The total vertical distanced traveled is given by $6 + 6 \left( \frac { 2 } { 5 } \right) + 2 ( 6 ) \left( \frac { 2 } { 5 } \right) ^ { 2 } + \ldots$ After the first term, the series is an infinite geometric series. Compute the total vertical distance traveled.

Accepted Answer

A)  The total vertical distance traveled is 10 ft. 
B)  The total vertical distance traveled is 14 ft. 
C)  The total vertical distance traveled is 4 ft. 
D)  The total vertical distance traveled is 8 ft. 
A)  The total vertical distance traveled is 10 ft. 
B)  The total vertical distance traveled is 14 ft. 
C)  The total vertical distance traveled is 4 ft. 
D)  The total vertical distance traveled is 8 ft.

Question 7

List the terms of the sequence. $$a _ { n } = 3 n - 8,1 \leq n \leq 4$$

Accepted Answer

A)  $- 5 , - 10 , - 15 , - 20$ 
B)  $- 5 , - 2,1,4$ 
C)  $5,10,15,20$ 
D)  $5,2 , - 1 , - 4$ 
A)  $- 5 , - 10 , - 15 , - 20$ 
B)  $- 5 , - 2,1,4$ 
C)  $5,10,15,20$ 
D)  $5,2 , - 1 , - 4$

Question 8

Find the number of terms, n, of the arithmetic sequence. $$- \frac { 5 } { 3 } , - 1 , - \frac { 1 } { 3 } , \ldots , \frac { 37 } { 3 }$$

Accepted Answer

A)  23 
B)  22 
C)  21 
D)  24 
A)  23 
B)  22 
C)  21 
D)  24

Question 9

Cameron deposited $650 in an account that pays 4% interest compounded annually. Write a sequence representing the amount Cameron receives in interest each year for the next 4 years. Round each term to the nearest cent.

Accepted Answer

A)  $26.00, $52.00, $78.00, 104.00 
B)  $26.00, $52.00, $104.00, $208.00 
C)  $26.00, $27.04, $28.12, $29.25 
D)  $26.00, $27.04, $27.46, $27.62 
A)  $26.00, $52.00, $78.00, 104.00 
B)  $26.00, $52.00, $104.00, $208.00 
C)  $26.00, $27.04, $28.12, $29.25 
D)  $26.00, $27.04, $27.46, $27.62

Question 10

Find a formula for the nth term of the sequence. $- 3,6 , - 9,12 , \ldots$

Accepted Answer

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

Question 11

Write the series in summation notation. $$z ^ { 5 } + z ^ { 10 } + z ^ { 15 } + z ^ { 20 } + z ^ { 25 }$$

Accepted Answer

A)  $\sum _ { j = 1 } ^ { 5 } z ^ { 5 j }$ 
B)  $\sum _ { j = 5 } ^ { 25 } z ^ { j }$ 
C)  $\sum _ { j = 5 } ^ { 9 } z ^ { j }$ 
D)  $\sum _ { j = 1 } ^ { 25 } z ^ { 5 j }$ 
A)  $\sum _ { j = 1 } ^ { 5 } z ^ { 5 j }$ 
B)  $\sum _ { j = 5 } ^ { 25 } z ^ { j }$ 
C)  $\sum _ { j = 5 } ^ { 9 } z ^ { j }$ 
D)  $\sum _ { j = 1 } ^ { 25 } z ^ { 5 j }$

Question 12

Find the sum of the arithmetic series. $$\sum _ { j = 1 } ^ { 21 } \left( \frac { 2 } { 3 } j + 1 \right)$$

Accepted Answer

A)  154 
B)  88 
C)  175 
D)  155 
A)  154 
B)  88 
C)  175 
D)  155

Question 13

Write the series in summation notation. $$1 + 2 + 3 + 4 + 5$$

Accepted Answer

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

Question 14

Expand the binomial. Use Pascal's triangle to find the coefficients. $$( 2 + y ) ^ { 4 }$$

Accepted Answer

A)  $16 + 8 y + 4 y ^ { 2 } + 2 y ^ { 3 } + y ^ { 4 }$ 
B)  $16 + 32 y + 24 y ^ { 2 } + 8 y ^ { 3 } + y ^ { 4 }$ 
C)  $16 + 4 y + 6 y ^ { 2 } + 4 y ^ { 3 } + y ^ { 4 }$ 
D)  $16 + y ^ { 4 }$ 
A)  $16 + 8 y + 4 y ^ { 2 } + 2 y ^ { 3 } + y ^ { 4 }$ 
B)  $16 + 32 y + 24 y ^ { 2 } + 8 y ^ { 3 } + y ^ { 4 }$ 
C)  $16 + 4 y + 6 y ^ { 2 } + 4 y ^ { 3 } + y ^ { 4 }$ 
D)  $16 + y ^ { 4 }$

Question 15

List the first five terms of the sequence. $a _ { 1 } = - 10 , a _ { n } = a _ { n - 1 } + 6$ for $n > 1$

Accepted Answer

A)  $- 10 , - 4,2,8,14$ 
B)  $7,13,19,25,31$ 
C)  $- 4,2,8,14,20$ 
D)  $1,7,13,19,25$ 
A)  $- 10 , - 4,2,8,14$ 
B)  $7,13,19,25,31$ 
C)  $- 4,2,8,14,20$ 
D)  $1,7,13,19,25$

Question 16

How many terms are in the expansion of $( v + w ) ^ { 15 }$ ?

Accepted Answer

A)  15 
B)  17 
C)  14 
D)  16 
A)  15 
B)  17 
C)  14 
D)  16

Question 17

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

Accepted Answer

A)  $- 4,16 , - 64,256$ 
B)  $4 , - 8,12 , - 16$ 
C)  $- 4,8 , - 12,16$ 
D)  $4 , - 16,64 , - 256$ 
A)  $- 4,16 , - 64,256$ 
B)  $4 , - 8,12 , - 16$ 
C)  $- 4,8 , - 12,16$ 
D)  $4 , - 16,64 , - 256$

Question 18

Find the twelfth term of the arithmetic sequence given $$a _ { 1 } = 4 \text { and } d = 7$$

Accepted Answer

A)  88 
B)  51 
C)  55 
D)  81 
A)  88 
B)  51 
C)  55 
D)  81

Question 19

Find the sum. $$\sum _ { i = 1 } ^ { 6 } ( 2 )$$

Accepted Answer

A)  6 
B)  10 
C)  12 
D)  8 
A)  6 
B)  10 
C)  12 
D)  8

Question 20

Find the sum. $$\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )$$

Accepted Answer

A)  -12 
B)  12 
C)  -84 
D)  84 
A)  -12 
B)  12 
C)  -84 
D)  84

Write the series in summation notation. $- \frac { 1 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 27 } + \frac { 1 } { 81 }$

Write the nth term of the arithmetic sequence. 3, -2, -7, -12, -17, ...

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

Find the sum. $\sum _ { i = 1 } ^ { 5 } \left( 2 i ^ { 2 } \right)$

Find the nth term of the geometric sequence. $\frac { 1 } { 2 } , 2,8,32 , \ldots$

List the terms of the sequence. $a _ { n } = 3 n - 8,1 \leq n \leq 4$

Find the number of terms, n, of the arithmetic sequence. $- \frac { 5 } { 3 } , - 1 , - \frac { 1 } { 3 } , \ldots , \frac { 37 } { 3 }$

Cameron deposited $650 in an account that pays 4% interest compounded annually. Write a sequence representing the amount Cameron receives in interest each year for the next 4 years. Round each term to the nearest cent.

Find a formula for the nth term of the sequence. $- 3,6 , - 9,12 , \ldots$

Write the series in summation notation. $z ^ { 5 } + z ^ { 10 } + z ^ { 15 } + z ^ { 20 } + z ^ { 25 }$

Find the sum of the arithmetic series. $\sum _ { j = 1 } ^ { 21 } \left( \frac { 2 } { 3 } j + 1 \right)$

Write the series in summation notation. $1 + 2 + 3 + 4 + 5$

Expand the binomial. Use Pascal's triangle to find the coefficients. $( 2 + y ) ^ { 4 }$

List the first five terms of the sequence. $a _ { 1 } = - 10 , a _ { n } = a _ { n - 1 } + 6$ for $n > 1$

How many terms are in the expansion of $( v + w ) ^ { 15 }$ ?

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

Find the twelfth term of the arithmetic sequence given $a _ { 1 } = 4 \text { and } d = 7$

Find the sum. $\sum _ { i = 1 } ^ { 6 } ( 2 )$

Find the sum. $\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )$

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Exam 10: Binomial Expansions, Sequences, and Series

Write the series in summation notation. −13+19−127+181- \frac { 1 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 27 } + \frac { 1 } { 81 }−31​+91​−271​+811​

Write the nth term of the arithmetic sequence. 3, -2, -7, -12, -17, ...

Write the first five terms of the arithmetic sequence. a1=−1,d=3a _ { 1 } = - 1 , d = 3a1​=−1,d=3

Find the sum. ∑i=15(2i2)\sum _ { i = 1 } ^ { 5 } \left( 2 i ^ { 2 } \right)∑i=15​(2i2)

Find the nth term of the geometric sequence. 12,2,8,32,…\frac { 1 } { 2 } , 2,8,32 , \ldots21​,2,8,32,…

List the terms of the sequence. an=3n−8,1≤n≤4a _ { n } = 3 n - 8,1 \leq n \leq 4an​=3n−8,1≤n≤4

Find the number of terms, n, of the arithmetic sequence. −53,−1,−13,…,373- \frac { 5 } { 3 } , - 1 , - \frac { 1 } { 3 } , \ldots , \frac { 37 } { 3 }−35​,−1,−31​,…,337​

Cameron deposited $650 in an account that pays 4% interest compounded annually. Write a sequence representing the amount Cameron receives in interest each year for the next 4 years. Round each term to the nearest cent.

Find a formula for the nth term of the sequence. −3,6,−9,12,…- 3,6 , - 9,12 , \ldots−3,6,−9,12,…

Write the series in summation notation. z5+z10+z15+z20+z25z ^ { 5 } + z ^ { 10 } + z ^ { 15 } + z ^ { 20 } + z ^ { 25 }z5+z10+z15+z20+z25

Find the sum of the arithmetic series. ∑j=121(23j+1)\sum _ { j = 1 } ^ { 21 } \left( \frac { 2 } { 3 } j + 1 \right)∑j=121​(32​j+1)

Write the series in summation notation. 1+2+3+4+51 + 2 + 3 + 4 + 51+2+3+4+5

Expand the binomial. Use Pascal's triangle to find the coefficients. (2+y)4( 2 + y ) ^ { 4 }(2+y)4

List the first five terms of the sequence. a1=−10,an=an−1+6a _ { 1 } = - 10 , a _ { n } = a _ { n - 1 } + 6a1​=−10,an​=an−1​+6 for n>1n > 1n>1

How many terms are in the expansion of (v+w)15( v + w ) ^ { 15 }(v+w)15 ?

List the terms of the sequence. an=(−1)n+14n,1≤n≤4a ^ { n } = ( - 1 ) ^ { n + 1 } 4 ^ { n } , 1 \leq n \leq 4an=(−1)n+14n,1≤n≤4

Find the twelfth term of the arithmetic sequence given a1=4 and d=7a _ { 1 } = 4 \text { and } d = 7a1​=4 and d=7

Find the sum. ∑i=16(2)\sum _ { i = 1 } ^ { 6 } ( 2 )∑i=16​(2)

Find the sum. ∑j=16(−1)j(4j)\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )∑j=16​(−1)j(4j)

Linear Equations and Inequalities in One Variable

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Write the series in summation notation. $- \frac { 1 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 27 } + \frac { 1 } { 81 }$

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

Find the sum. $\sum _ { i = 1 } ^ { 5 } \left( 2 i ^ { 2 } \right)$

Find the nth term of the geometric sequence. $\frac { 1 } { 2 } , 2,8,32 , \ldots$

List the terms of the sequence. $a _ { n } = 3 n - 8,1 \leq n \leq 4$

Find the number of terms, n, of the arithmetic sequence. $- \frac { 5 } { 3 } , - 1 , - \frac { 1 } { 3 } , \ldots , \frac { 37 } { 3 }$

Find a formula for the nth term of the sequence. $- 3,6 , - 9,12 , \ldots$

Write the series in summation notation. $z ^ { 5 } + z ^ { 10 } + z ^ { 15 } + z ^ { 20 } + z ^ { 25 }$

Find the sum of the arithmetic series. $\sum _ { j = 1 } ^ { 21 } \left( \frac { 2 } { 3 } j + 1 \right)$

Write the series in summation notation. $1 + 2 + 3 + 4 + 5$

Expand the binomial. Use Pascal's triangle to find the coefficients. $( 2 + y ) ^ { 4 }$

List the first five terms of the sequence. $a _ { 1 } = - 10 , a _ { n } = a _ { n - 1 } + 6$ for $n > 1$

How many terms are in the expansion of $( v + w ) ^ { 15 }$ ?

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

Find the twelfth term of the arithmetic sequence given $a _ { 1 } = 4 \text { and } d = 7$

Find the sum. $\sum _ { i = 1 } ^ { 6 } ( 2 )$

Find the sum. $\sum _ { j = 1 } ^ { 6 } ( - 1 ) ^ { j } ( 4 j )$