Question 1

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = - 2 ( n + 2 ) !$$

Accepted Answer

A)  $- 12,96 , - 720,5760$ 
B)  $- 4 , - 24 , - 144 , - 960$ 
C)  $- 12 , - 48 , - 240 , - 1440$ 
D)  $- 4,12 , - 48,240$ 
A)  $- 12,96 , - 720,5760$ 
B)  $- 4 , - 24 , - 144 , - 960$ 
C)  $- 12 , - 48 , - 240 , - 1440$ 
D)  $- 4,12 , - 48,240$ C

Question 2

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { \mathrm { i } = 1 } ^ { 48 } ( 4 \mathrm { i } + 7 )$$

Accepted Answer

A)  4944 
B)  5184 
C)  5040 
D)  5352 
A)  4944 
B)  5184 
C)  5040 
D)  5352 C

Question 3

Find the indicated sum.
-$\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } ( k + 1 )$

Accepted Answer

A)  -14 
B)  6 
C)  2 
D)  14 
A)  -14 
B)  6 
C)  2 
D)  14 C

Question 4

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \frac { 4 } { n ^ { 2 } }$$

Accepted Answer

A)  $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 }$ 
B)  $1 , \frac { 2 } { 4 } , \frac { 3 } { 9 } , \frac { 4 } { 16 }$ 
C)  $4 , \frac { 4 } { 4 } , \frac { 4 } { 9 } , \frac { 4 } { 16 }$ 
D)  $\frac { 4 } { 4 } , \frac { 4 } { 9 } , \frac { 4 } { 16 } , \frac { 4 } { 25 }$ 
A)  $1 , \frac { 1 } { 4 } , \frac { 1 } { 9 } , \frac { 1 } { 16 }$ 
B)  $1 , \frac { 2 } { 4 } , \frac { 3 } { 9 } , \frac { 4 } { 16 }$ 
C)  $4 , \frac { 4 } { 4 } , \frac { 4 } { 9 } , \frac { 4 } { 16 }$ 
D)  $\frac { 4 } { 4 } , \frac { 4 } { 9 } , \frac { 4 } { 16 } , \frac { 4 } { 25 }$

Question 5

Find the indicated sum.
-$$\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } - 1 ) ! } { ( \mathrm { i } + 2 ) ! }$$

Accepted Answer

A)  $\frac { 37 } { 30 }$ 
B)  $\frac { 241 } { 140 }$ 
C)  $\frac { 43 } { 20 }$ 
D)  $\frac { 5 } { 21 }$ 
A)  $\frac { 37 } { 30 }$ 
B)  $\frac { 241 } { 140 }$ 
C)  $\frac { 43 } { 20 }$ 
D)  $\frac { 5 } { 21 }$

Question 6

Find the indicated sum.
-$$\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 4 i }$$

Accepted Answer

A)  $\frac { 11 } { 24 }$ 
B)  $\frac { 5 } { 16 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  $\frac { 25 } { 48 }$ 
A)  $\frac { 11 } { 24 }$ 
B)  $\frac { 5 } { 16 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  $\frac { 25 } { 48 }$

Question 7

Solve the problem.
-Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $130 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at
The end of her first year.

Accepted Answer

A)  $a _ { n } = 2870 + 130 n ; \$ 4430$ 
B)  $a _ { n } = 3000 + 130 n ; \$ 4560$ 
C)  $a _ { n } = 3000 + 130 n ; \$ 4430$ 
D)  $a _ { n } = 2870 + 130 ( n - 1 ) ; \$ 4300$ 
A)  $a _ { n } = 2870 + 130 n ; \$ 4430$ 
B)  $a _ { n } = 3000 + 130 n ; \$ 4560$ 
C)  $a _ { n } = 3000 + 130 n ; \$ 4430$ 
D)  $a _ { n } = 2870 + 130 ( n - 1 ) ; \$ 4300$

Question 8

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 13 } { 15 }$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 13 } \frac { i } { i + 2 }$ 
B)  $\sum _ { i = 0 } ^ { 13 } \frac { i } { i + 2 }$ 
C)  $\sum _ { i = 2 } ^ { 13 } \frac { i } { i + 1 }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { \mathrm { n } } \frac { \mathrm { i } } { \mathrm { i } + 2 }$ 
A)  $\sum _ { i = 1 } ^ { 13 } \frac { i } { i + 2 }$ 
B)  $\sum _ { i = 0 } ^ { 13 } \frac { i } { i + 2 }$ 
C)  $\sum _ { i = 2 } ^ { 13 } \frac { i } { i + 1 }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { \mathrm { n } } \frac { \mathrm { i } } { \mathrm { i } + 2 }$

Question 9

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = n ^ { 2 } - n$$

Accepted Answer

A)  $2,6,12,20$ 
B)  $0,2,6,12$ 
C)  $1,4,9,16$ 
D)  $0,3,8,15$ 
A)  $2,6,12,20$ 
B)  $0,2,6,12$ 
C)  $1,4,9,16$ 
D)  $0,3,8,15$

Question 10

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = n - 6$$

Accepted Answer

A)  $- 5 , - 4 , - 3 , - 2$ 
B)  $1,2,3,4$ 
C)  $- 6 , - 5 , - 4 , - 3$ 
D)  $- 24 , - 18 , - 12 , - 6$ 
A)  $- 5 , - 4 , - 3 , - 2$ 
B)  $1,2,3,4$ 
C)  $- 6 , - 5 , - 4 , - 3$ 
D)  $- 24 , - 18 , - 12 , - 6$

Question 11

Solve the problem.
-A new exhibit is scheduled to open at the local museum. Museum officials expect that 8000 people will visit the exhibit in its first week, and that the number of visitors will drop by 30 people per week after the first week
During the first 6 months. Find the total number of visitors expected in the exhibit's first 7 weeks.

Accepted Answer

A)  47,550 visitors 
B)  55,370 visitors 
C)  39,550 visitors 
D)  55,190 visitors 
A)  47,550 visitors 
B)  55,370 visitors 
C)  39,550 visitors 
D)  55,190 visitors

Question 12

Find the indicated sum.
-$$\sum _ { i = 9 } ^ { 12 } \frac { 1 } { i + 3 }$$

Accepted Answer

A)  $- \frac { 323 } { 660 }$ 
B)  $\frac { 820 } { 2187 }$ 
C)  54 
D)  $\frac { 543 } { 1820 }$ 
A)  $- \frac { 323 } { 660 }$ 
B)  $\frac { 820 } { 2187 }$ 
C)  54 
D)  $\frac { 543 } { 1820 }$

Question 13

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \frac { n } { n ^ { 2 } + 2 }$$

Accepted Answer

A)  $\frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$ 
B)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 }$ 
C)  $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 }$ 
D)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 }$ 
A)  $\frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$ 
B)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 }$ 
C)  $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 }$ 
D)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 }$

Question 14

Find the indicated sum.
-$\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } + 8 \right)$

Accepted Answer

A)  48 
B)  36 
C)  74 
D)  95 
A)  48 
B)  36 
C)  74 
D)  95

Question 15

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \left( \frac { 2 } { 3 } \right) ^ { n }$$

Accepted Answer

A)  $1 , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
B)  $\frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
C)  $1 , \frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 }$ 
D)  $\frac { 2 } { 3 } , \frac { 2 } { 6 } , \frac { 2 } { 9 } , \frac { 2 } { 12 }$ 
A)  $1 , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
B)  $\frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 } , \frac { 16 } { 81 }$ 
C)  $1 , \frac { 2 } { 3 } , \frac { 4 } { 9 } , \frac { 8 } { 27 }$ 
D)  $\frac { 2 } { 3 } , \frac { 2 } { 6 } , \frac { 2 } { 9 } , \frac { 2 } { 12 }$

Question 16

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
--21, -26 , -31, -36, . . .

Accepted Answer

A)  $a _ { n } = 5 n + 16 ; a _ { 20 } = 116$ 
B)  $a _ { n } = 5 n + 21 ; a _ { 20 } = 121$ 
C)  $a _ { n } = - 5 n - 16 ; a _ { 20 } = - 116$ 
D)  $a _ { n } = - 5 n - 21 ; a _ { 20 } = - 121$ 
A)  $a _ { n } = 5 n + 16 ; a _ { 20 } = 116$ 
B)  $a _ { n } = 5 n + 21 ; a _ { 20 } = 121$ 
C)  $a _ { n } = - 5 n - 16 ; a _ { 20 } = - 116$ 
D)  $a _ { n } = - 5 n - 21 ; a _ { 20 } = - 121$

Question 17

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \frac { ( n + 1 ) ! } { n ^ { 4 } }$$

Accepted Answer

A)  $2 , \frac { 3 } { 8 } , \frac { 8 } { 27 } , \frac { 15 } { 32 }$ 
B)  $2 , \frac { 3 } { 8 } , \frac { 4 } { 27 } , \frac { 5 } { 64 }$ 
C)  $\frac { 1 } { 2 } , \frac { 3 } { 4 } , 2 , \frac { 15 } { 2 }$ 
D)  $\frac { 1 } { 2 } , \frac { 3 } { 4 } , 1 , \frac { 5 } { 4 }$ 
A)  $2 , \frac { 3 } { 8 } , \frac { 8 } { 27 } , \frac { 15 } { 32 }$ 
B)  $2 , \frac { 3 } { 8 } , \frac { 4 } { 27 } , \frac { 5 } { 64 }$ 
C)  $\frac { 1 } { 2 } , \frac { 3 } { 4 } , 2 , \frac { 15 } { 2 }$ 
D)  $\frac { 1 } { 2 } , \frac { 3 } { 4 } , 1 , \frac { 5 } { 4 }$

Question 18

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first eight terms of the arithmetic sequence: 10, 15, 20, . . . .

Accepted Answer

A)  220 
B)  45 
C)  120 
D)  440 
A)  220 
B)  45 
C)  120 
D)  440

Question 19

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \frac { n ^ { 3 } } { ( n - 1 ) ! }$$

Accepted Answer

A)  $\frac { 3 } { 0 } , \frac { 6 } { 0 } , \frac { 9 } { 2 } , 2$ 
B)  $1,8 , \frac { 27 } { 2 } , \frac { 32 } { 3 }$ 
C)  $\frac { 1 } { 0 } , \frac { 8 } { 0 } , \frac { 27 } { 2 } , \frac { 32 } { 3 }$ 
D)  $3,6 , \frac { 9 } { 2 } , 2$ 
A)  $\frac { 3 } { 0 } , \frac { 6 } { 0 } , \frac { 9 } { 2 } , 2$ 
B)  $1,8 , \frac { 27 } { 2 } , \frac { 32 } { 3 }$ 
C)  $\frac { 1 } { 0 } , \frac { 8 } { 0 } , \frac { 27 } { 2 } , \frac { 32 } { 3 }$ 
D)  $3,6 , \frac { 9 } { 2 } , 2$

Question 20

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
-$$5 + 6 + 7 + 8 + \ldots + 34$$

Accepted Answer

A)  $\sum _ { k = 1 } ^ { 29 } ( k - 1 )$ 
B)  $\sum _ { k = 4 } ^ { 33 } ( k - 1 )$ 
C)  $\sum _ { k = 5 } ^ { 34 } ( k - 1 )$ 
D)  $\sum _ { k = 6 } ^ { 35 } ( k - 1 )$ 
A)  $\sum _ { k = 1 } ^ { 29 } ( k - 1 )$ 
B)  $\sum _ { k = 4 } ^ { 33 } ( k - 1 )$ 
C)  $\sum _ { k = 5 } ^ { 34 } ( k - 1 )$ 
D)  $\sum _ { k = 6 } ^ { 35 } ( k - 1 )$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = - 2 ( n + 2 ) !$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { \mathrm { i } = 1 } ^ { 48 } ( 4 \mathrm { i } + 7 )$

Find the indicated sum. - $\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } ( k + 1 )$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$

Find the indicated sum. - $\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } - 1 ) ! } { ( \mathrm { i } + 2 ) ! }$

Find the indicated sum. - $\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 4 i }$

Solve the problem. -Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $130 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at The end of her first year.

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 13 } { 15 }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = n ^ { 2 } - n$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = n - 6$

Find the indicated sum. - $\sum _ { i = 9 } ^ { 12 } \frac { 1 } { i + 3 }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { n } { n ^ { 2 } + 2 }$

Find the indicated sum. - $\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } + 8 \right)$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \left( \frac { 2 } { 3 } \right) ^ { n }$

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20, the 20th term of the sequence. --21, -26 , -31, -36, . . .

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { ( n + 1 ) ! } { n ^ { 4 } }$

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first eight terms of the arithmetic sequence: 10, 15, 20, . . . .

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { n ^ { 3 } } { ( n - 1 ) ! }$

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $5 + 6 + 7 + 8 + \ldots + 34$

Variables, Real Numbers, and Mathematical Models

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Factoring Polynomials

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Exam 10: Radicals, Radical Functions, and Rational Exponents

Write the first four terms of the sequence whose general term is given. - an=−2(n+2)!a _ { n } = - 2 ( n + 2 ) !an​=−2(n+2)!

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - ∑i=148(4i+7)\sum _ { \mathrm { i } = 1 } ^ { 48 } ( 4 \mathrm { i } + 7 )∑i=148​(4i+7)

Find the indicated sum. - ∑k=14(−1)k(k+1)\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } ( k + 1 )∑k=14​(−1)k(k+1)

Write the first four terms of the sequence whose general term is given. - an=4n2a _ { n } = \frac { 4 } { n ^ { 2 } }an​=n24​

Find the indicated sum. - ∑i=15(i−1)!(i+2)!\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } - 1 ) ! } { ( \mathrm { i } + 2 ) ! }∑i=15​(i+2)!(i−1)!​

Find the indicated sum. - ∑i=1414i\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 4 i }∑i=14​4i1​