Question 1

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

Accepted Answer

A)  3, 4, 5, 6 
B)  0, 2, 4, 6 
C)  2, 4, 6, 8 
D)  1, 0, -1, -2 
A)  3, 4, 5, 6 
B)  0, 2, 4, 6 
C)  2, 4, 6, 8 
D)  1, 0, -1, -2

Question 2

Solve the problem.
-The population of a town is increasing by 300 inhabitants each year. If its current population is 20,506 and this trend continues, what would its population be in 8 years?

Accepted Answer

A)  22,606 inhabitants 
B)  163,964 inhabitants 
C)  22,906 inhabitants 
D)  327,928 inhabitants 
A)  22,606 inhabitants 
B)  163,964 inhabitants 
C)  22,906 inhabitants 
D)  327,928 inhabitants

Question 3

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

Accepted Answer

A)  -2, -4, -6, -8, -10 
B)  -2, 2, 6, 10, 14 
C)  -1, 1, 3, 5, 7 
D)  -6, -2, 2, 6, 10 
A)  -2, -4, -6, -8, -10 
B)  -2, 2, 6, 10, 14 
C)  -1, 1, 3, 5, 7 
D)  -6, -2, 2, 6, 10

Question 4

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$6 ^ { 2 } + 12 ^ { 3 } + 18 ^ { 4 } + \ldots + 48 ^ { 9 }$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 8 } 6 i ^ { 2 i } - 1$ 
B)  $\sum _ { i = 1 } ^ { 8 } ( 6 i ) ^ { i } + 1$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 8 } 2 ( \mathrm { i } - 1 ) ^ { \mathrm { i } + 1 }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 8 } ( 6 \mathrm { i } ) ^ { \mathrm { i } }$ 
A)  $\sum _ { i = 1 } ^ { 8 } 6 i ^ { 2 i } - 1$ 
B)  $\sum _ { i = 1 } ^ { 8 } ( 6 i ) ^ { i } + 1$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 8 } 2 ( \mathrm { i } - 1 ) ^ { \mathrm { i } + 1 }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 8 } ( 6 \mathrm { i } ) ^ { \mathrm { i } }$

Question 5

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-$$\text { Find } a _ { 10 } \text { when } a _ { 1 } = 2 , r = 2$$

Accepted Answer

A)  1024 
B)  1028 
C)  20 
D)  2048 
A)  1024 
B)  1028 
C)  20 
D)  2048

Question 6

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

Accepted Answer

A)  19 
B)  26 
C)  34 
D)  30 
A)  19 
B)  26 
C)  34 
D)  30

Question 7

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 27 } ( 6 i - 1 )$$

Accepted Answer

A)  $2362.5$ 
B)  2457 
C)  2241 
D)  2160 
A)  $2362.5$ 
B)  2457 
C)  2241 
D)  2160

Question 8

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
-a1 = 9; d = 5

Accepted Answer

A)  9, 13, 17, 21, 25 
B)  0, 9, 14, 19, 24 
C)  14, 19, 24, 29, 34 
D)  9, 14, 19, 24, 29 
A)  9, 13, 17, 21, 25 
B)  0, 9, 14, 19, 24 
C)  14, 19, 24, 29, 34 
D)  9, 14, 19, 24, 29

Question 9

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$a + a r + a r ^ { 2 } + \ldots + a r ^ { 10 }$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 10 } a r ^ { i }$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 10 } \left( \mathrm { ar } ^ { \mathrm { i } } - 1 \right.$ 
C)  $\sum _ { i = 1 } ^ { 11 } a r ^ { i - 1 }$ 
D)  $\sum _ { i = 1 } ^ { 10 } ( a r ) ^ { i }$ 
A)  $\sum _ { i = 1 } ^ { 10 } a r ^ { i }$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 10 } \left( \mathrm { ar } ^ { \mathrm { i } } - 1 \right.$ 
C)  $\sum _ { i = 1 } ^ { 11 } a r ^ { i - 1 }$ 
D)  $\sum _ { i = 1 } ^ { 10 } ( a r ) ^ { i }$

Question 10

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d.
-Find a8 when a1 = -9 , d = 4 .

Accepted Answer

A)  -41 
B)  -37 
C)  23 
D)  19 
A)  -41 
B)  -37 
C)  23 
D)  19

Question 11

Write out the first three terms and the last term of the arithmetic sequence.
-$$\sum _ { i = 1 } ^ { 70 } - 2 i$$

Accepted Answer

A)  $- 2 + 4 - 12 + \ldots - 280$ 
B)  $- 1 - 2 - 4 - \ldots - 140$ 
C)  $- 2 - 4 - 8 - \ldots - 280$ 
D)  $- 2 - 4 - 6 - \ldots - 140$ 
A)  $- 2 + 4 - 12 + \ldots - 280$ 
B)  $- 1 - 2 - 4 - \ldots - 140$ 
C)  $- 2 - 4 - 8 - \ldots - 280$ 
D)  $- 2 - 4 - 6 - \ldots - 140$

Question 12

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r.
-$$a _ { 1 } = 6 ; r = 2$$

Accepted Answer

A)  $6,8,10,12 , \ldots$ 
B)  $2,12,72,432 , \ldots$ 
C)  $12,24,48,96 , \ldots$ 
D)  $6,12,24,48 , \ldots$ 
A)  $6,8,10,12 , \ldots$ 
B)  $2,12,72,432 , \ldots$ 
C)  $12,24,48,96 , \ldots$ 
D)  $6,12,24,48 , \ldots$

Question 13

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d.
-$$a _ { 1 } = \frac { 7 } { 2 } , d = \frac { 5 } { 2 }$$

Accepted Answer

A)  $\frac { 7 } { 2 } , 6 , \frac { 17 } { 2 } , 11 , \frac { 27 } { 2 }$ 
B)  $\frac { 7 } { 2 } , 1 , - \frac { 3 } { 2 } , - 4 , - \frac { 13 } { 2 }$ 
C)  $\frac { 7 } { 2 } , \frac { 1 } { 2 } , - \frac { 1 } { 2 } , - 1 , - \frac { 13 } { 10 }$ 
D)  $\frac { 7 } { 2 } , 3 , \frac { 17 } { 6 } , \frac { 11 } { 4 } , \frac { 27 } { 10 }$ 
A)  $\frac { 7 } { 2 } , 6 , \frac { 17 } { 2 } , 11 , \frac { 27 } { 2 }$ 
B)  $\frac { 7 } { 2 } , 1 , - \frac { 3 } { 2 } , - 4 , - \frac { 13 } { 2 }$ 
C)  $\frac { 7 } { 2 } , \frac { 1 } { 2 } , - \frac { 1 } { 2 } , - 1 , - \frac { 13 } { 10 }$ 
D)  $\frac { 7 } { 2 } , 3 , \frac { 17 } { 6 } , \frac { 11 } { 4 } , \frac { 27 } { 10 }$

Question 14

Solve the problem.
-As part of her retirement savings plan, Patricia deposited $350 in a bank account during her first year in the workforce. During each subsequent year, she deposited $50 more than the previous year. Find how much she deposited during her twentieth year in the workforce. Find the total amount deposited in the twenty years.

Accepted Answer

A)  $1300; $33,000 
B)  $1350; $17,000 
C)  $1300; $16,500 
D)  $1350; $34,000 
A)  $1300; $33,000 
B)  $1350; $17,000 
C)  $1300; $16,500 
D)  $1350; $34,000

Question 15

Solve the problem.
-A deposit of $8000 is made in an account that earns 5.2% interest compounded quarterly. The balance in the account after n quarters is given by the sequence an = 8000(1 + 0.0524 )n, n = 1, 2, 3, ... Find the balance in the account after six years by computing a24

Accepted Answer

A)  $8180.46 
B)  $10,907.29 
C)  $6946.46 
D)  $8644.63 
A)  $8180.46 
B)  $10,907.29 
C)  $6946.46 
D)  $8644.63

Question 16

Use the partial sum formula to find the partial sum of the given arithmetic sequence.
-Find the sum of the first five terms of the arithmetic sequence: -10, -14, -18, . . . .

Accepted Answer

A)  -70 
B)  90 
C)  - 90 
D)  -42 
A)  -70 
B)  90 
C)  - 90 
D)  -42

Question 17

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
-Find $a _ { 6 }$ when $a _ { 1 } = 3200 , r = - \frac { 1 } { 2 }$.

Accepted Answer

A)  100 
B)  $- 100$ 
C)  $- 50$ 
D)  $- 10$ 
A)  100 
B)  $- 100$ 
C)  $- 50$ 
D)  $- 10$

Question 18

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \frac { n ^ { 2 } } { ( n - 1 ) ! }$$

Accepted Answer

A)  $1,4 , \frac { 9 } { 2 } , \frac { 8 } { 3 }$ 
B)  $2,4,3 , \frac { 4 } { 3 }$ 
C)  $\frac { 2 } { 0 } , \frac { 4 } { 0 } , 3 , \frac { 4 } { 3 }$ 
D)  $\frac { 1 } { 0 } , \frac { 4 } { 0 } , \frac { 9 } { 2 } , \frac { 8 } { 3 }$ 
A)  $1,4 , \frac { 9 } { 2 } , \frac { 8 } { 3 }$ 
B)  $2,4,3 , \frac { 4 } { 3 }$ 
C)  $\frac { 2 } { 0 } , \frac { 4 } { 0 } , 3 , \frac { 4 } { 3 }$ 
D)  $\frac { 1 } { 0 } , \frac { 4 } { 0 } , \frac { 9 } { 2 } , \frac { 8 } { 3 }$

Question 19

Solve the problem.
-A new exhibit is scheduled to open at the local museum. Museum officials expect that 7000 people will visit the exhibit in its first week, and that the number of visitors will drop by 10 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)  48,790 visitors 
B)  41,850 visitors 
C)  48,730 visitors 
D)  34,850 visitors 
A)  48,790 visitors 
B)  41,850 visitors 
C)  48,730 visitors 
D)  34,850 visitors

Question 20

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation.
-$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }$$

Accepted Answer

A)  $\sum _ { \mathrm { k } = 1 } ^ { 15 } a r ^ { \mathrm { k } }$ 
B)  $\sum _ { k = 0 } ^ { 15 } a r ^ { k }$ 
C)  $\sum _ { \mathrm { k } = 1 } ^ { 16 } a \mathrm { r } ^ { \mathrm { k } }$ 
D)  $\sum _ { k = 0 } ^ { 15 } ( a r ) ^ { k }$ 
A)  $\sum _ { \mathrm { k } = 1 } ^ { 15 } a r ^ { \mathrm { k } }$ 
B)  $\sum _ { k = 0 } ^ { 15 } a r ^ { k }$ 
C)  $\sum _ { \mathrm { k } = 1 } ^ { 16 } a \mathrm { r } ^ { \mathrm { k } }$ 
D)  $\sum _ { k = 0 } ^ { 15 } ( a r ) ^ { k }$

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

Solve the problem. -The population of a town is increasing by 300 inhabitants each year. If its current population is 20,506 and this trend continues, what would its population be in 8 years?

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

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $6 ^ { 2 } + 12 ^ { 3 } + 18 ^ { 4 } + \ldots + 48 ^ { 9 }$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - $\text { Find } a _ { 10 } \text { when } a _ { 1 } = 2 , r = 2$

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

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 27 } ( 6 i - 1 )$

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d. -a1 = 9; d = 5

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $a + a r + a r ^ { 2 } + \ldots + a r ^ { 10 }$

Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a8 when a₁ = -9 , d = 4 .

Write out the first three terms and the last term of the arithmetic sequence. - $\sum _ { i = 1 } ^ { 70 } - 2 i$

Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. - $a _ { 1 } = 6 ; r = 2$

Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d. - $a _ { 1 } = \frac { 7 } { 2 } , d = \frac { 5 } { 2 }$

Solve the problem. -A deposit of $8000 is made in an account that earns 5.2% interest compounded quarterly. The balance in the account after n quarters is given by the sequence an = 8000(1 + 0.0524 )n, n = 1, 2, 3, ... Find the balance in the account after six years by computing a24

Use the partial sum formula to find the partial sum of the given arithmetic sequence. -Find the sum of the first five terms of the arithmetic sequence: -10, -14, -18, . . . .

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find $a _ { 6 }$ when $a _ { 1 } = 3200 , r = - \frac { 1 } { 2 }$ .

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { n ^ { 2 } } { ( n - 1 ) ! }$

Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of summation. - $a + a r + a r ^ { 2 } + \ldots + a r ^ { 15 }$

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Exam 8: Quadratic Equations and Functions

Write the first four terms of the sequence whose general term is given. - an=2na _ { n } = 2 nan​=2n

Solve the problem. -The population of a town is increasing by 300 inhabitants each year. If its current population is 20,506 and this trend continues, what would its population be in 8 years?

Write the first four terms of the sequence whose general term is given. - an=2(2n−3)a _ { n } = 2 ( 2 n - 3 )an​=2(2n−3)

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - 62+123+184+…+4896 ^ { 2 } + 12 ^ { 3 } + 18 ^ { 4 } + \ldots + 48 ^ { 9 }62+123+184+…+489

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. - Find a10 when a1=2,r=2\text { Find } a _ { 10 } \text { when } a _ { 1 } = 2 , r = 2 Find a10​ when a1​=2,r=2

Find the indicated sum. - ∑i=25(3i−2)\sum _ { i = 2 } ^ { 5 } ( 3 i - 2 )∑i=25​(3i−2)

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - ∑i=127(6i−1)\sum _ { i = 1 } ^ { 27 } ( 6 i - 1 )∑i=127​(6i−1)